Average Error: 0.1 → 0.1
Time: 4.4s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \left(\log z + 1\right) + 0.5 \cdot x\right) - z \cdot y\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \left(\log z + 1\right) + 0.5 \cdot x\right) - z \cdot y
double code(double x, double y, double z) {
	return ((double) (((double) (x * 0.5)) + ((double) (y * ((double) (((double) (1.0 - z)) + ((double) log(z))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (y * ((double) (((double) log(z)) + 1.0)))) + ((double) (0.5 * x)))) - ((double) (z * y))));
}

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

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020162 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"
  :precision binary64

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

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))