Average Error: 0.1 → 0.1
Time: 3.9s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + y \cdot \log \left(\sqrt[3]{z}\right)\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) (x * 0.5)) + ((double) (((double) (y * ((double) (((double) (((double) (2.0 * ((double) log(((double) cbrt(z)))))) + 1.0)) - z)))) + ((double) (y * ((double) log(((double) cbrt(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 add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied associate-+r+0.1

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

  6. Simplified0.1

    \[\leadsto x \cdot 0.5 + y \cdot \left(\color{blue}{\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right)} + \log \left(\sqrt[3]{z}\right)\right)\]
  7. Using strategy rm

  8. Applied distribute-lft-in0.1

    \[\leadsto x \cdot 0.5 + \color{blue}{\left(y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)}\]

  9. Final simplification0.1

    \[\leadsto x \cdot 0.5 + \left(y \cdot \left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + 1\right) - z\right) + y \cdot \log \left(\sqrt[3]{z}\right)\right)\]

Reproduce

herbie shell --seed 2020150 
(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)))))