Average Error: 12.4 → 0.7
Time: 2.6s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.85881602499750145 \cdot 10^{307}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.35754709924995739 \cdot 10^{114}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.2951699973466196 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.9950788779712852 \cdot 10^{303}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{{\left(\frac{y}{y - z}\right)}^{3}}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.85881602499750145 \cdot 10^{307}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.35754709924995739 \cdot 10^{114}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.2951699973466196 \cdot 10^{54}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.9950788779712852 \cdot 10^{303}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\sqrt[3]{{\left(\frac{y}{y - z}\right)}^{3}}}\\

\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 ((((double) (((double) (x * ((double) (y - z)))) / y)) <= -2.8588160249975014e+307)) {
		VAR = ((double) (x / ((double) (y / ((double) (y - z))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= -1.3575470992499574e+114)) {
			VAR_1 = ((double) (((double) (x * ((double) (y - z)))) / y));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.2951699973466196e+54)) {
				VAR_2 = ((double) (x / ((double) (y / ((double) (y - z))))));
			} else {
				double VAR_3;
				if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 1.9950788779712852e+303)) {
					VAR_3 = ((double) (((double) (x * ((double) (y - z)))) / y));
				} else {
					VAR_3 = ((double) (x / ((double) cbrt(((double) pow(((double) (y / ((double) (y - z)))), 3.0))))));
				}
				VAR_2 = VAR_3;
			}
			VAR_1 = VAR_2;
		}
		VAR = VAR_1;
	}
	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

Original12.4
Target3.2
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -2.85881602499750145e307 or -1.35754709924995739e114 < (/ (* x (- y z)) y) < 1.2951699973466196e54

    1. Initial program 11.9

      \[\frac{x \cdot \left(y - z\right)}{y}\]
    2. Using strategy rm

    3. Applied associate-/l*0.6

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

    if -2.85881602499750145e307 < (/ (* x (- y z)) y) < -1.35754709924995739e114 or 1.2951699973466196e54 < (/ (* x (- y z)) y) < 1.9950788779712852e303

    1. Initial program 0.2

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

    if 1.9950788779712852e303 < (/ (* x (- y z)) y)

    1. Initial program 61.7

      \[\frac{x \cdot \left(y - z\right)}{y}\]
    2. Using strategy rm

    3. Applied associate-/l*0.5

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

    5. Applied add-cbrt-cube58.8

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

    6. Applied add-cbrt-cube59.1

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

    7. Applied cbrt-undiv59.1

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

    8. Simplified4.0

      \[\leadsto \frac{x}{\sqrt[3]{\color{blue}{{\left(\frac{y}{y - z}\right)}^{3}}}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -2.85881602499750145 \cdot 10^{307}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.35754709924995739 \cdot 10^{114}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.2951699973466196 \cdot 10^{54}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 1.9950788779712852 \cdot 10^{303}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{{\left(\frac{y}{y - z}\right)}^{3}}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(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))