Average Error: 0.1 → 0.1
Time: 3.3s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + \left(\left(\log \left(\sqrt[3]{z}\right) \cdot 2 + \left(1 - z\right)\right) \cdot y + y \cdot \log \left({z}^{0.3333333333333333}\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + \left(\left(\log \left(\sqrt[3]{z}\right) \cdot 2 + \left(1 - z\right)\right) \cdot y + y \cdot \log \left({z}^{0.3333333333333333}\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)
  (+
   (* (+ (* (log (cbrt z)) 2.0) (- 1.0 z)) y)
   (* y (log (pow z 0.3333333333333333))))))
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) (((double) (((double) (((double) log(((double) cbrt(z)))) * 2.0)) + ((double) (1.0 - z)))) * y)) + ((double) (y * ((double) log(((double) pow(z, 0.3333333333333333))))))))));
}

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 Error: 0.1 bits

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

  3. Applied add-cube-cbrtError: 0.1 bits

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

  4. Applied log-prodError: 0.1 bits

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

  5. Applied associate-+r+Error: 0.1 bits

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

  6. SimplifiedError: 0.1 bits

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

  8. Applied distribute-lft-inError: 0.1 bits

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

  9. SimplifiedError: 0.1 bits

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

  10. SimplifiedError: 0.1 bits

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

  12. Applied pow1/3Error: 0.1 bits

    \[\leadsto x \cdot 0.5 + \left(\left(\log \left(\sqrt[3]{z}\right) \cdot 2 + \left(1 - z\right)\right) \cdot y + \log \color{blue}{\left({z}^{0.3333333333333333}\right)} \cdot y\right)\]

  13. Final simplificationError: 0.1 bits

    \[\leadsto x \cdot 0.5 + \left(\left(\log \left(\sqrt[3]{z}\right) \cdot 2 + \left(1 - z\right)\right) \cdot y + y \cdot \log \left({z}^{0.3333333333333333}\right)\right)\]

Reproduce

herbie shell --seed 2020204 
(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)))))