Average Error: 0.1 → 0.1
Time: 7.1s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y - y \cdot \left(z - \log z\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y - y \cdot \left(z - \log z\right)\right)
(FPCore (x y z) :precision binary64 (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))
↓
(FPCore (x y z) :precision binary64 (+ (* x 0.5) (- y (* y (- z (log z))))))
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 (x * 0.5) + (y - (y * (z - log(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
\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

  1. Initial program 0.1

    \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
  2. Using strategy rm

  3. Applied distribute-rgt-in_binary64_68480.1

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

  4. Simplified0.1

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

  6. Applied associate-+l-_binary64_68330.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2021015 
(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)))))