Average Error: 0.1 → 0.1
Time: 6.9s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(\log \left(\sqrt{z}\right) + \left(1 - z\right)\right) + y \cdot \log \left(\sqrt{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(\log \left(\sqrt{z}\right) + \left(1 - z\right)\right) + y \cdot \log \left(\sqrt{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 (+ (log (sqrt z)) (- 1.0 z))) (* y (log (sqrt 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 * (log(sqrt(z)) + (1.0 - z))) + (y * log(sqrt(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_105990.1

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

  4. Simplified0.1

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

  5. Simplified0.1

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

  7. Applied add-sqr-sqrt_binary64_106710.1

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

  8. Applied log-prod_binary64_107350.1

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

  9. Applied distribute-rgt-in_binary64_105990.1

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

  10. Applied associate-+r+_binary64_105810.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020342 
(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)))))