Average Error: 10.1 → 1.2
Time: 3.9s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\left(x \cdot \left(\sqrt[3]{y + 1} \cdot \frac{\sqrt[3]{y + 1}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y + 1}}{\sqrt[3]{z}} - x\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\left(x \cdot \left(\sqrt[3]{y + 1} \cdot \frac{\sqrt[3]{y + 1}}{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right)\right) \cdot \frac{\sqrt[3]{y + 1}}{\sqrt[3]{z}} - x
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * ((double) (((double) cbrt(((double) (y + 1.0)))) * ((double) (((double) cbrt(((double) (y + 1.0)))) / ((double) (((double) cbrt(z)) * ((double) cbrt(z)))))))))) * ((double) (((double) cbrt(((double) (y + 1.0)))) / ((double) cbrt(z)))))) - x));
}

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

Original10.1
Target0.4
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Initial program 10.1

    \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]

  2. Simplified3.2

    \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} - x}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt3.8

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

  5. Applied add-cube-cbrt3.8

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

  6. Applied times-frac3.8

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

  7. Applied associate-*r*1.2

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

  8. Simplified1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))