R2 Score is incorect

[fabienmorgan]

Setup: I have cloned your project and also cloned the provided weights. I created a new environment with Python 3.8.10 and installed like the README suggests pip install -r requirements.txt. I couldn't build the wheel of pycocotools so I commented it out of the requirements. The code ran perfectly fine.

Issue: After running the suggested example, python -m MMSR predict --model /path/to/MMSR-model 'x**2 + x' three times I got a wrong R2 score for at least two runs. The whole output is at the end of the description, but the relevant part of the free runs can be seen right below: python -m MMSR predict --model /model 'x* Output:

Function: (y+((sin(x))^3))
R2: 0.9930888206580541
Relative error: 1.5958611854800162

python -m MMSR predict --model model 'x**2 + x' Output:

Function: (y+sin(x))
R2: 1.0
Relative error: 0.0

python -m MMSR predict --model model 'x**2 + x' Output

Function: (y+sin(x))
R2: 1.0
Relative error: 0.0

Now multiple questions came up. Firstly, it seems to be that the R2 score gets calculated wrongly. There is no case where the R2 score of two different equations give 1.0. Even in cases where the equation is mathematically the same but the order of the operators changes, it can happen that the equation doesn't return a R2 score of 1.0. Another question that rises from this output is what is y in the equation? Does the predicted equation (y+sin(x)) meany=sin(x), did the prediction invent another variable, is y a placeholder for a constant or does y have an other meaning? The last question is about the relative error. I couldn't find the explanation to this value in the repository, so my question is, is this the mean relative error over all sampled points?

(mmsr_original_tensorflow) fmg@T7144:~/repos/FMg_SR_Bachelor_Thesis/Original_MMSR$ python -m MMSR predict --model model 'x**
2 + x'
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
2024-05-22 20:55:32.926712: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.085856: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.086099: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.086551: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-05-22 20:55:33.087589: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.087771: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.087927: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.138024: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.138288: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.138493: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:33.138617: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1525] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 7358 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3080, pci bus id: 0000:33:00.0, compute capability: 8.6
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
2024-05-22 20:55:41.402690: I tensorflow/stream_executor/cuda/cuda_blas.cc:1786] TensorFloat-32 will be used for the matrix multiplication. This will only be logged once.
2024-05-22 20:55:41.683170: I tensorflow/stream_executor/cuda/cuda_dnn.cc:368] Loaded cuDNN version 8907
2024-05-22 20:55:44.926375: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:44.964434: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:44.964624: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:44.964976: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-05-22 20:55:44.965859: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:44.966022: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:44.966148: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:45.012541: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:45.012705: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:45.012829: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:55:45.012942: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1525] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 1069 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3080, pci bus id: 0000:33:00.0, compute capability: 8.6
Function: (y+((sin(x))^3))
R2: 0.9930888206580541
Relative error: 1.5958611854800162
WARNING:tensorflow:Detecting that an object or model or tf.train.Checkpoint is being deleted with unrestored values. See the following logs for the specific values in question. To silence these warnings, use `status.expect_partial()`. See https://www.tensorflow.org/api_docs/python/tf/train/Checkpoint#restorefor details about the status object returned by the restore function.
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.beta_1
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.beta_2
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.decay
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.iter
(mmsr_original_tensorflow) fmg@T7144:~/repos/FMg_SR_Bachelor_Thesis/Original_MMSR$ python -m MMSR predict --model model 'x**2 + x'
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
2024-05-22 20:58:15.042666: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.084969: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.085179: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.085577: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-05-22 20:58:15.086594: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.086733: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.086847: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.134471: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.134652: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.134794: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:15.134921: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1525] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 7352 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3080, pci bus id: 0000:33:00.0, compute capability: 8.6
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
2024-05-22 20:58:23.183359: I tensorflow/stream_executor/cuda/cuda_blas.cc:1786] TensorFloat-32 will be used for the matrix multiplication. This will only be logged once.
2024-05-22 20:58:23.229171: I tensorflow/stream_executor/cuda/cuda_dnn.cc:368] Loaded cuDNN version 8907
2024-05-22 20:58:25.897060: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.936908: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.937186: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.937673: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-05-22 20:58:25.938930: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.939064: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.939179: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.983866: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.984031: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.984153: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:58:25.984265: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1525] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 1067 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3080, pci bus id: 0000:33:00.0, compute capability: 8.6
Function: (y+sin(x))
R2: 1.0
Relative error: 0.0
WARNING:tensorflow:Detecting that an object or model or tf.train.Checkpoint is being deleted with unrestored values. See the following logs for the specific values in question. To silence these warnings, use `status.expect_partial()`. See https://www.tensorflow.org/api_docs/python/tf/train/Checkpoint#restorefor details about the status object returned by the restore function.
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.beta_1
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.beta_2
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.decay
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.iter
(mmsr_original_tensorflow) fmg@T7144:~/repos/FMg_SR_Bachelor_Thesis/Original_MMSR$ python -m MMSR predict --model model 'x**2 + x'
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
2024-05-22 20:59:13.489857: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.528914: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.529110: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.529479: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-05-22 20:59:13.530632: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.530868: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.531065: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.586527: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.586766: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.586955: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:13.587092: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1525] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 7350 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3080, pci bus id: 0000:33:00.0, compute capability: 8.6
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
self.num_heads: 12
self.d_model: 384
0
2024-05-22 20:59:21.613165: I tensorflow/stream_executor/cuda/cuda_blas.cc:1786] TensorFloat-32 will be used for the matrix multiplication. This will only be logged once.
2024-05-22 20:59:21.654994: I tensorflow/stream_executor/cuda/cuda_dnn.cc:368] Loaded cuDNN version 8907
2024-05-22 20:59:24.353759: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.391157: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.391377: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.391749: I tensorflow/core/platform/cpu_feature_guard.cc:151] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  AVX2 FMA
To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
2024-05-22 20:59:24.392717: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.392860: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.392985: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.440845: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.441046: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.441186: I tensorflow/stream_executor/cuda/cuda_gpu_executor.cc:936] successful NUMA node read from SysFS had negative value (-1), but there must be at least one NUMA node, so returning NUMA node zero
2024-05-22 20:59:24.441310: I tensorflow/core/common_runtime/gpu/gpu_device.cc:1525] Created device /job:localhost/replica:0/task:0/device:GPU:0 with 1069 MB memory:  -> device: 0, name: NVIDIA GeForce RTX 3080, pci bus id: 0000:33:00.0, compute capability: 8.6
Function: (y+sin(x))
R2: 1.0
Relative error: 0.0
WARNING:tensorflow:Detecting that an object or model or tf.train.Checkpoint is being deleted with unrestored values. See the following logs for the specific values in question. To silence these warnings, use `status.expect_partial()`. See https://www.tensorflow.org/api_docs/python/tf/train/Checkpoint#restorefor details about the status object returned by the restore function.
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.beta_1
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.beta_2
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.decay
WARNING:tensorflow:Value in checkpoint could not be found in the restored object: (root).optimizer.iter

[1716757342]

Dear colleagues, thank you very much for your interest in our work. We have done a test to solve your problem, and there seems to be no problem in our test.

os.environ = 3 2024-05-23 17:21:14.511827: ... $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ os.environ = 3 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ os.environ = 3 Function: (x+((x)^2)) R2: 1.0 Relative error: 5.303451293530877e-17

You can also specify the expression you want to test in predict.py and then run the code with python predict.py. I wish you a happy life.

[1716757342]

os.environ = 3 2024-05-23 17:28:51.094565: ... $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ os.environ = 3 $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ os.environ = 3 Function: (x+((x)^2)) R2: 1.0 Relative error: 3.016847939590277e-17

[fabienmorgan]

Looking further in the code, it seems that the predict function doesn't take an equation as an argument and just predicts the equation sin(x) + y. There is no indication of using any of the arguments that were put in and the line function = 'sin(x) + y' (Line 18) indicate that it takes this hardcoded equation. This would also answer the question of why it returned the following output with an R2 of 1.0 for this command python -m MMSR predict --model model 'x**2 + x':

Function: (y+sin(x))
R2: 1.0
Relative error: 0.0

Can you confirm that this is the case or if it is not the case to tell me what this hardcoded equation does in the predict.py?