Average Error: 12.6 → 2.3
Time: 1.6s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.11290955006504583 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \le 1.1301515707540782 \cdot 10^{111}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;z \le 2.52593401718285492 \cdot 10^{184}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;z \le -2.11290955006504583 \cdot 10^{-28}:\\
\;\;\;\;x - \frac{z}{\frac{y}{x}}\\

\mathbf{elif}\;z \le 1.1301515707540782 \cdot 10^{111}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;z \le 2.52593401718285492 \cdot 10^{184}:\\
\;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x * (y - z)) / y);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if ((z <= -2.112909550065046e-28)) {
		VAR = (x - (z / (y / x)));
	} else {
		double VAR_1;
		if ((z <= 1.1301515707540782e+111)) {
			VAR_1 = (x / (y / (y - z)));
		} else {
			double VAR_2;
			if ((z <= 2.525934017182855e+184)) {
				VAR_2 = (1.0 / (y / (x * (y - z))));
			} else {
				VAR_2 = (x - (z / (y / x)));
			}
			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

Original12.6
Target2.8
Herbie2.3
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -2.112909550065046e-28 or 2.525934017182855e+184 < z

    1. Initial program 11.6

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

    3. Applied *-commutative11.6

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

    4. Applied associate-/l*11.2

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

    6. Applied div-sub11.2

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

    7. Simplified5.0

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

    if -2.112909550065046e-28 < z < 1.1301515707540782e+111

    1. Initial program 13.1

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

    3. Applied associate-/l*0.4

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

    if 1.1301515707540782e+111 < z < 2.525934017182855e+184

    1. Initial program 11.4

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

    3. Applied clear-num11.5

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

  4. Final simplification2.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.11290955006504583 \cdot 10^{-28}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \mathbf{elif}\;z \le 1.1301515707540782 \cdot 10^{111}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;z \le 2.52593401718285492 \cdot 10^{184}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z}{\frac{y}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020078 
(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))