Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + y \cdot \log \left(\sqrt[3]{z}\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + y \cdot \log \left(\sqrt[3]{z}\right)
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) (1.0 - z)) + ((double) log(((double) (((double) cbrt(z)) * ((double) cbrt(z)))))))))) + ((double) (x * 0.5)))) + ((double) (y * ((double) log(((double) cbrt(z))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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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-lft-in0.1

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

  4. Applied associate-+r+0.1

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

  6. Applied add-cube-cbrt0.1

    \[\leadsto \left(x \cdot 0.5 + y \cdot \left(1 - z\right)\right) + y \cdot \log \color{blue}{\left(\left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{z}\right)}\]

  7. Applied log-prod0.1

    \[\leadsto \left(x \cdot 0.5 + y \cdot \left(1 - z\right)\right) + y \cdot \color{blue}{\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)}\]

  8. Applied distribute-lft-in0.1

    \[\leadsto \left(x \cdot 0.5 + y \cdot \left(1 - z\right)\right) + \color{blue}{\left(y \cdot \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\]

  9. Applied associate-+r+0.1

    \[\leadsto \color{blue}{\left(\left(x \cdot 0.5 + y \cdot \left(1 - z\right)\right) + y \cdot \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + y \cdot \log \left(\sqrt[3]{z}\right)}\]

  10. Simplified0.1

    \[\leadsto \color{blue}{\left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right)} + y \cdot \log \left(\sqrt[3]{z}\right)\]

  11. Final simplification0.1

    \[\leadsto \left(y \cdot \left(\left(1 - z\right) + \log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right) + x \cdot 0.5\right) + y \cdot \log \left(\sqrt[3]{z}\right)\]

Reproduce

herbie shell --seed 2020130 
(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)))))