Average Error: 0.1 → 0.1
Time: 5.7s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[{\left(x + \left(y - \log y \cdot \left(0.5 + y\right)\right)\right)}^{1} - z\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
{\left(x + \left(y - \log y \cdot \left(0.5 + y\right)\right)\right)}^{1} - z
double code(double x, double y, double z) {
	return (((x - ((y + 0.5) * log(y))) + y) - z);
}
↓
double code(double x, double y, double z) {
	return (pow((x + (y - (log(y) * (0.5 + y)))), 1.0) - z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

    \[\leadsto \color{blue}{\left(x + \left(y - \log y \cdot \left(0.5 + y\right)\right)\right)} - z\]
  4. Using strategy rm

  5. Applied pow10.1

    \[\leadsto \color{blue}{{\left(x + \left(y - \log y \cdot \left(0.5 + y\right)\right)\right)}^{1}} - z\]

  6. Final simplification0.1

    \[\leadsto {\left(x + \left(y - \log y \cdot \left(0.5 + y\right)\right)\right)}^{1} - z\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))