Average Error: 0.1 → 0.1
Time: 6.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(\left(x \cdot 2\right) \cdot \left(\log \left({y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right) - y\right) - \left(z - \log t\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(\left(x \cdot 2\right) \cdot \left(\log \left({y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right) - y\right) - \left(z - \log t\right)
double code(double x, double y, double z, double t) {
	return ((((x * log(y)) - y) - z) + log(t));
}
↓
double code(double x, double y, double z, double t) {
	return (((((x * 2.0) * (log(pow(y, 0.3333333333333333)) + log(cbrt(cbrt(y))))) + (log(cbrt(cbrt(y))) * x)) - y) - (z - log(t)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
  2. Using strategy rm

  3. Applied associate-+l-0.1

    \[\leadsto \color{blue}{\left(x \cdot \log y - y\right) - \left(z - \log t\right)}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot \log \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - y\right) - \left(z - \log t\right)\]

  6. Applied log-prod0.1

    \[\leadsto \left(x \cdot \color{blue}{\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right)} - y\right) - \left(z - \log t\right)\]

  7. Applied distribute-lft-in0.1

    \[\leadsto \left(\color{blue}{\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right)} - y\right) - \left(z - \log t\right)\]

  8. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) - y\right) - \left(z - \log t\right)\]
  9. Using strategy rm

  10. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot \sqrt[3]{\sqrt[3]{y}}\right)}\right) - y\right) - \left(z - \log t\right)\]

  11. Applied log-prod0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)}\right) - y\right) - \left(z - \log t\right)\]

  12. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)}\right) - y\right) - \left(z - \log t\right)\]

  13. Applied associate-+r+0.1

    \[\leadsto \left(\color{blue}{\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)} - y\right) - \left(z - \log t\right)\]

  14. Simplified0.1

    \[\leadsto \left(\left(\color{blue}{\left(x \cdot 2\right) \cdot \left(\log \left({y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)} + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right) - y\right) - \left(z - \log t\right)\]

  15. Final simplification0.1

    \[\leadsto \left(\left(\left(x \cdot 2\right) \cdot \left(\log \left({y}^{\frac{1}{3}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right) - y\right) - \left(z - \log t\right)\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))