Average Error: 12.6 → 2.0
Time: 3.5s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.7425772490475051 \cdot 10^{41} \lor \neg \left(z \le 2435460001394761700\right) \land z \le 2.58559422776367219 \cdot 10^{201}:\\ \;\;\;\;x - \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.7425772490475051 \cdot 10^{41} \lor \neg \left(z \le 2435460001394761700\right) \land z \le 2.58559422776367219 \cdot 10^{201}:\\
\;\;\;\;x - \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}\\

\mathbf{else}:\\
\;\;\;\;x - x \cdot \frac{z}{y}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (y - z)))) / y));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.742577249047505e+41) || (!(z <= 2.4354600013947617e+18) && (z <= 2.585594227763672e+201)))) {
		VAR = ((double) (x - ((double) (((double) (x / ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))) * ((double) (z / ((double) cbrt(y))))))));
	} else {
		VAR = ((double) (x - ((double) (x * ((double) (z / 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

Original12.6
Target3.2
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.7425772490475051e41 or 2435460001394761700 < z < 2.58559422776367219e201

    1. Initial program 11.1

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

    2. Simplified7.6

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

    4. Applied add-cube-cbrt8.2

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

    5. Applied *-un-lft-identity8.2

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

    6. Applied times-frac8.2

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

    7. Applied associate-*r*3.6

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

    8. Simplified3.6

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

    if -1.7425772490475051e41 < z < 2435460001394761700 or 2.58559422776367219e201 < z

    1. Initial program 13.3

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

    2. Simplified1.2

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.7425772490475051 \cdot 10^{41} \lor \neg \left(z \le 2435460001394761700\right) \land z \le 2.58559422776367219 \cdot 10^{201}:\\ \;\;\;\;x - \frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))