x+x does not simplify to 2x

[andrew-murdza]

Code

    import { ComputeEngine } from 'https://unpkg.com/@cortex-js/compute-engine?module';
    const ce = new ComputeEngine();
    const expr1 = ce.parse('x+x', { canonical: false });
    const simplifiedExpr1 = expr1.simplify();
    console.log(simplifiedExpr1.toString());

Actual Behavior

x+x

Expected Behavior

2x

[andrew-murdza]

Bugs that are harder to fix

• \frac{0}{1-1} and \frac{1-1}{0} (\frac{0}{0} works)
• 2(x+h)^2-2x^2 ((x+h)^2-x^2 and 2(x+h)(x+h)-x^2 work)
• \frac{\pi+1}{\pi+1} (\frac{\pi}{\pi} works)
• \frac{x^2}{5x^2} (\frac{5x^2}{x^2} works)
• (-1)^{3/5} (should be -1 not i)
• \frac{\frac{1}{x^6}}{\frac{1}{y^4}} becomes \frac{y^4}{x^6} (good) but \left(\frac{x^3}{y^2}\right)^{-2} becomes \frac{\frac{1}{x^6}}{\frac{1}{y^4}} (should be \frac{y^4}{x^6})
• exp(x)exp(2) (e^xe^2 works)
• \frac{x+1-1+1}{x+1} (\frac{x+1-1+1}{x} works)
• (-2x)^{3/5}x simplifies to (i)\sqrt{2}x^{8/5} not -2^{3/5}x^{8/5} ((2x)^{3/5}x works)
• (x^3y^2)^2 ((x^3)^2(y^2)^2 and \left(\frac{x^3}{y^2}\right)^2 work)
• \frac{2\sqrt{3}}{\sqrt{3}} becomes 2 (good) but \frac{\sqrt{12x}}{\sqrt{3x}} becomes \frac{2\sqrt{3}}{\sqrt{3}}
• \sqrt{12} (\frac{\sqrt{12x}}{\sqrt{x}} works)
• \sqrt{x^2y}
• \sqrt{x^2}, \sqrt[4]{x^4} (missing absolute value)
• \sqrt[4]{x^6} (missing absolute value inside of root)

Logs

• log(e^xy) (ln(e^xy) works)
• ln(\frac{x}{y}) (log(\frac{x}{y}) works)
• log(xy)-log(x)-log(y) (ln(xy)-ln(x)-ln(y) works)
• log(1) (ln(1) works)
• log(e) (ln(e) works)
• exp(log(x))
• exp(clog(x))
• exp(log(x)+y)
• exp(log(x)-y)
• log(exp(x)) (ln(exp(x)) works)
• \log(\sqrt{2}) and \ln(\sqrt{2}) (\log(\sqrt{x}) and \ln(\sqrt{x}) work)

Negative Signs

• (-x)(-6)
• -\frac{-1}{x} (\frac{-1}{-x} works)
• (-x)^2 ((-2x)^2 works)

Properties of Exponents

• 2xx (xx works)
• \frac{e^x}{e}
• \frac{e}{e^x}
• e^xe and e^xe^1 (e^xe^2 works)
• \left(\frac{1}{x}\right)^{-1}

Other Powers

• 0^0
• 0^\pi (0^{3.1} works)

Infinity

• \infty^0
• \infty(1-1) (\infty(0) works)
• 1^\infty
• -\infty(-2) and \infty(-2) (-\infty(2) and \infty(2) work)
• \frac{\infty}{2}
• \frac{\infty}{\infty}
• \frac{\infty}{\infty^{-2}}

Miscellaneous

• \frac{1}{0}

Trig

• sec(-x) is 1/cos(x) but I believe sec(x) is nicer
• Similarly for csc(pi+x), tan(pi/2-x), sec(pi/2-x), csc(pi/2-x)
• cot(pi+x) is supposed to be cot(x) but set to -cot(x)
• tan(-x)cot(x) becomes -tan(x)cot(x) and tan(x)cot(x) becomes 1 but tan(-x)cot(x) doesn't become -1
• sin^2(x) is simplified to 1/2(1-cos(2x)) but 2sin^2(x) is not simplified at all
• sin(x)cos(x) is simplified to sin(2x)/2 but 2sin(x)cos(x) is not simplified at all