Average Error: 10.0 → 0.2
Time: 3.1s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -1.8104924256738275 \cdot 10^{-84} \lor \neg \left(x \leq 7.274545131975547 \cdot 10^{-145}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -1.8104924256738275 \cdot 10^{-84} \lor \neg \left(x \leq 7.274545131975547 \cdot 10^{-145}\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\

\end{array}
double code(double x, double y, double z) {
	return (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((x <= -1.8104924256738275e-84) || !(x <= 7.274545131975547e-145))) {
		VAR = ((double) (((double) ((x / z) * ((double) (y + 1.0)))) - x));
	} else {
		VAR = (((double) (x * ((double) (1.0 + ((double) (y - z)))))) / z);
	}
	return VAR;
}

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

Original10.0
Target0.5
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -1.81049242567382748e-84 or 7.2745451319755472e-145 < x

    1. Initial program 16.4

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

    2. Simplified1.1

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

    4. Applied *-un-lft-identity1.1

      \[\leadsto x \cdot \frac{y + 1}{\color{blue}{1 \cdot z}} - x\]

    5. Applied add-cube-cbrt1.4

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

    6. Applied times-frac1.4

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

    7. Applied associate-*r*3.3

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

    8. Simplified3.3

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

    9. Taylor expanded around 0 5.2

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

    10. Simplified0.3

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

    if -1.81049242567382748e-84 < x < 7.2745451319755472e-145

    1. Initial program 0.2

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8104924256738275 \cdot 10^{-84} \lor \neg \left(x \leq 7.274545131975547 \cdot 10^{-145}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(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))