Average Error: 0.1 → 0.1
Time: 7.4s
Precision: binary64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot {y}^{\frac{1}{3}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x - y\right)\right) - z\right) + \log t
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (x * ((double) log(y)))) - y)) - z)) + ((double) log(t))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (x * ((double) log(((double) (((double) cbrt(y)) * ((double) pow(y, 0.3333333333333333)))))))) + ((double) (((double) (((double) log(((double) cbrt(y)))) * x)) - y)))) - z)) + ((double) log(t))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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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 add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020147 
(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)))