Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\left(x \cdot \log y - y\right) + \left(\log t - z\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\left(x \cdot \log y - y\right) + \left(\log t - z\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 * log(y)) - y) + (log(t) - 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 0.1

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

  3. Applied sub-neg0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

    \[\leadsto \left(x \cdot \log y - y\right) + \left(\log t - z\right)\]

Reproduce

herbie shell --seed 2020106 
(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)))