Average Error: 0.1 → 0.1
Time: 4.2s
Precision: binary64
\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
↓
\[x \cdot 0.5 + y \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{z}}\right) + \left(\left(1 - z\right) + 2 \cdot \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)\right)\right)\]
x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)
↓
x \cdot 0.5 + y \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{z}}\right) + \left(\left(1 - z\right) + 2 \cdot \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{\sqrt[3]{z}}\right)\right)\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 (cbrt (cbrt z)))
    (+ (- 1.0 z) (* 2.0 (+ (log (cbrt z)) (log (cbrt (cbrt 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(cbrt(cbrt(z))) + ((1.0 - z) + (2.0 * (log(cbrt(z)) + log(cbrt(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-cbrt_binary640.1

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

  4. Applied log-prod_binary640.1

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

  5. Applied associate-+r+_binary640.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt_binary640.1

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

  9. Applied log-prod_binary640.1

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

  10. Applied associate-+r+_binary640.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020253 
(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)))))