Average Error: 0.3 → 0.3
Time: 9.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t
double code(double x, double y, double z, double t, double a) {
	return (((log((x + y)) + log(z)) - t) + ((a - 0.5) * log(t)));
}
↓
double code(double x, double y, double z, double t, double a) {
	return ((((pow(log((x + y)), 3.0) + pow(log(z), 3.0)) / ((log(z) * (log(z) - log((x + y)))) + (log((x + y)) * log((x + y))))) - t) + ((a - 0.5) * log(t)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied flip3-+0.3

    \[\leadsto \left(\color{blue}{\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log \left(x + y\right) \cdot \log \left(x + y\right) + \left(\log z \cdot \log z - \log \left(x + y\right) \cdot \log z\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  4. Simplified0.3

    \[\leadsto \left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\color{blue}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)}} - t\right) + \left(a - 0.5\right) \cdot \log t\]

  5. Final simplification0.3

    \[\leadsto \left(\frac{{\left(\log \left(x + y\right)\right)}^{3} + {\left(\log z\right)}^{3}}{\log z \cdot \left(\log z - \log \left(x + y\right)\right) + \log \left(x + y\right) \cdot \log \left(x + y\right)} - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2020071 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))