Average Error: 13.1 → 2.7
Time: 2.7s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.2799990873646843 \cdot 10^{-221} \lor \neg \left(y \leq 3.5017718189801225 \cdot 10^{-168}\right):\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.2799990873646843 \cdot 10^{-221} \lor \neg \left(y \leq 3.5017718189801225 \cdot 10^{-168}\right):\\
\;\;\;\;x - x \cdot \frac{z}{y}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}\\

\end{array}
double code(double x, double y, double z) {
	return (((double) (x * ((double) (y - z)))) / y);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((y <= -1.2799990873646843e-221) || !(y <= 3.5017718189801225e-168))) {
		VAR = ((double) (x - ((double) (x * (z / y)))));
	} else {
		VAR = ((double) (x - ((double) ((x / ((double) (((double) cbrt(y)) * ((double) cbrt(y))))) * (z / ((double) cbrt(y)))))));
	}
	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

Original13.1
Target3.3
Herbie2.7
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.2799990873646843e-221 or 3.50177181898012248e-168 < y

    1. Initial program 13.2

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

    2. Simplified1.6

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

    if -1.2799990873646843e-221 < y < 3.50177181898012248e-168

    1. Initial program 12.3

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

    2. Simplified12.2

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

    4. Applied add-cube-cbrt12.9

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

    5. Applied *-un-lft-identity12.9

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

    6. Applied times-frac12.9

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

    7. Applied associate-*r*9.3

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

    8. Simplified9.3

      \[\leadsto x - \color{blue}{\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}}} \cdot \frac{z}{\sqrt[3]{y}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2799990873646843 \cdot 10^{-221} \lor \neg \left(y \leq 3.5017718189801225 \cdot 10^{-168}\right):\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z)
  :name "Diagrams.Backend.Cairo.Internal:setTexture from diagrams-cairo-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< z -2.060202331921739e+104) (- x (/ (* z x) y)) (if (< z 1.6939766013828526e+213) (/ x (/ y (- y z))) (* (- y z) (/ x y))))

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