Average Error: 12.8 → 2.2
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -9.8715650386691714 \cdot 10^{295} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.40955937979382073 \cdot 10^{116}\right):\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -9.8715650386691714 \cdot 10^{295} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.40955937979382073 \cdot 10^{116}\right):\\
\;\;\;\;x - x \cdot \frac{z}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{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 ((((((double) (x * ((double) (y - z)))) / y) <= -9.871565038669171e+295) || !((((double) (x * ((double) (y - z)))) / y) <= -2.4095593797938207e+116))) {
		VAR = ((double) (x - ((double) (x * (z / y)))));
	} else {
		VAR = (((double) (x * ((double) (y - 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

Original12.8
Target3.1
Herbie2.2
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < -9.8715650386691714e295 or -2.40955937979382073e116 < (/ (* x (- y z)) y)

    1. Initial program 14.4

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

    2. Simplified2.5

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

    if -9.8715650386691714e295 < (/ (* x (- y z)) y) < -2.40955937979382073e116

    1. Initial program 0.2

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

  4. Final simplification2.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -9.8715650386691714 \cdot 10^{295} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -2.40955937979382073 \cdot 10^{116}\right):\\ \;\;\;\;x - x \cdot \frac{z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))