Average Error: 12.5 → 2.8
Time: 1.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -4.39403416583893017 \cdot 10^{-211} \lor \neg \left(y \le 1.6466713287575296 \cdot 10^{-176}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -4.39403416583893017 \cdot 10^{-211} \lor \neg \left(y \le 1.6466713287575296 \cdot 10^{-176}\right):\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

\mathbf{else}:\\
\;\;\;\;x - \frac{x \cdot 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 (((y <= -4.39403416583893e-211) || !(y <= 1.6466713287575296e-176))) {
		VAR = ((double) (x * ((double) (1.0 - ((double) (z / y))))));
	} else {
		VAR = ((double) (x - ((double) (((double) (x * 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

Original12.5
Target3.3
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.39403416583893e-211 or 1.6466713287575296e-176 < y

    1. Initial program 12.6

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

    3. Applied *-un-lft-identity12.6

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

    4. Applied times-frac1.9

      \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y - z}{y}}\]

    5. Simplified1.9

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

    7. Applied div-sub1.8

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

    8. Simplified1.8

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

    if -4.39403416583893e-211 < y < 1.6466713287575296e-176

    1. Initial program 11.9

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

    3. Applied associate-/l*12.3

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

    4. Taylor expanded around 0 9.1

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

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -4.39403416583893017 \cdot 10^{-211} \lor \neg \left(y \le 1.6466713287575296 \cdot 10^{-176}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020121 
(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))