Average Error: 12.5 → 0.2
Time: 3.0s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -28669507326513398000:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.40912979358746977 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.08452281427565051 \cdot 10^{301}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -28669507326513398000:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.40912979358746977 \cdot 10^{-11}:\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.08452281427565051 \cdot 10^{301}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

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

\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 ((((x * (y - z)) / y) <= -inf.0)) {
		VAR = ((x / y) * (y - z));
	} else {
		double VAR_1;
		if ((((x * (y - z)) / y) <= -2.8669507326513398e+19)) {
			VAR_1 = ((x * (y - z)) / y);
		} else {
			double VAR_2;
			if ((((x * (y - z)) / y) <= 2.4091297935874698e-11)) {
				VAR_2 = (x * (1.0 - (z / y)));
			} else {
				double VAR_3;
				if ((((x * (y - z)) / y) <= 2.0845228142756505e+301)) {
					VAR_3 = ((x * (y - z)) / y);
				} else {
					VAR_3 = (x * (1.0 - (z / y)));
				}
				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

Original12.5
Target3.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (* x (- y z)) y) < -inf.0

    1. Initial program 64.0

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

    3. Applied associate-/l*0.1

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

    5. Applied associate-/r/0.1

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

    if -inf.0 < (/ (* x (- y z)) y) < -2.8669507326513398e+19 or 2.4091297935874698e-11 < (/ (* x (- y z)) y) < 2.0845228142756505e+301

    1. Initial program 0.2

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

    if -2.8669507326513398e+19 < (/ (* x (- y z)) y) < 2.4091297935874698e-11 or 2.0845228142756505e+301 < (/ (* x (- y z)) y)

    1. Initial program 14.6

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

    3. Applied *-un-lft-identity14.6

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

    4. Applied times-frac0.3

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

    5. Simplified0.3

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

    7. Applied div-sub0.3

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

    8. Simplified0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} = -\infty:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le -28669507326513398000:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.40912979358746977 \cdot 10^{-11}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.08452281427565051 \cdot 10^{301}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020103 +o rules:numerics
(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))