Average Error: 0.1 → 0.1
Time: 8.3s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right) \]
↓
\[\left(\log z \cdot y + \left(y + 0.5 \cdot x\right)\right) - z \cdot y \]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(\log z \cdot y + \left(y + 0.5 \cdot x\right)\right) - z \cdot y

(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))
↓
(FPCore (x y z)
 :precision binary64
 (- (+ (* (log z) y) (+ y (* 0.5 x))) (* z y)))
double code(double x, double y, double z) {
	return (x * 0.5) + (y * ((1.0 - z) + log(z)));
}
↓
double code(double x, double y, double z) {
	return ((log(z) * y) + (y + (0.5 * x))) - (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. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, 0.5, \mathsf{fma}\left(y, \log z - z, y\right)\right)} \]

  3. Taylor expanded in x around 0 0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2021357 
(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)))))