Average Error: 0.1 → 0.1
Time: 3.4s
Precision: binary64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt[3]{t}\right) + \left(\left(x \cdot \log y - y\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot 2 - z\right)\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt[3]{t}\right) + \left(\left(x \cdot \log y - y\right) + \left(\log \left(\sqrt[3]{t}\right) \cdot 2 - z\right)\right)
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) log(((double) cbrt(t)))) + ((double) (((double) (((double) (x * ((double) log(y)))) - y)) + ((double) (((double) (((double) log(((double) cbrt(t)))) * 2.0)) - z))))));
}

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 Error: 0.1 bits

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

  3. Applied add-cube-cbrtError: 0.1 bits

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

  4. Applied log-prodError: 0.1 bits

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

  5. Applied associate-+r+Error: 0.1 bits

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

  6. SimplifiedError: 0.1 bits

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

  7. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020200 
(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)))