Average Error: 12.8 → 2.1
Time: 5.4s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -8.712739772132689 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;x \le 4.6822193034122338 \cdot 10^{-163}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;x \le -8.712739772132689 \cdot 10^{-76}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;x \le 4.6822193034122338 \cdot 10^{-163}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

\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 ((x <= -8.712739772132689e-76)) {
		VAR = (x / (y / ((double) (y - z))));
	} else {
		double VAR_1;
		if ((x <= 4.682219303412234e-163)) {
			VAR_1 = ((double) (x - (((double) (x * z)) / y)));
		} else {
			VAR_1 = ((double) (x * ((double) (1.0 - (z / y)))));
		}
		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

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

Derivation

  1. Split input into 3 regimes

  2. if x < -8.712739772132689e-76

    1. Initial program 17.6

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

    3. Applied associate-/l*0.5

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

    if -8.712739772132689e-76 < x < 4.6822193034122338e-163

    1. Initial program 7.2

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

    2. Taylor expanded around 0 3.6

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

    if 4.6822193034122338e-163 < x

    1. Initial program 14.8

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

    3. Applied *-un-lft-identity14.8

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

    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-sub1.9

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

    8. Simplified1.9

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

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.712739772132689 \cdot 10^{-76}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;x \le 4.6822193034122338 \cdot 10^{-163}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array}\]

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))