Average Error: 12.9 → 1.9
Time: 2.7s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.271300469497502 \cdot 10^{69}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.55259092160079069 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.22149086807395917 \cdot 10^{294}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.271300469497502 \cdot 10^{69}:\\
\;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.55259092160079069 \cdot 10^{-42}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.22149086807395917 \cdot 10^{294}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\

\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 ((((double) (((double) (x * ((double) (y - z)))) / y)) <= -5.271300469497502e+69)) {
		VAR = ((double) (((double) (x / y)) * ((double) (y - z))));
	} else {
		double VAR_1;
		if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 2.5525909216007907e-42)) {
			VAR_1 = ((double) (x * ((double) (((double) (y - z)) / y))));
		} else {
			double VAR_2;
			if ((((double) (((double) (x * ((double) (y - z)))) / y)) <= 3.221490868073959e+294)) {
				VAR_2 = ((double) (((double) (x * ((double) (y - z)))) / y));
			} else {
				VAR_2 = ((double) (1.0 / ((double) (((double) (y / ((double) (y - z)))) / 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

Original12.9
Target3.1
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ (* x (- y z)) y) < -5.271300469497502e+69

    1. Initial program 20.7

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

    3. Applied associate-/l*5.7

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

    5. Applied associate-/r/6.5

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

    if -5.271300469497502e+69 < (/ (* x (- y z)) y) < 2.5525909216007907e-42

    1. Initial program 6.7

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

    3. Applied *-un-lft-identity6.7

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

    4. Applied times-frac0.4

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

    5. Simplified0.4

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

    if 2.5525909216007907e-42 < (/ (* x (- y z)) y) < 3.221490868073959e+294

    1. Initial program 0.2

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

    if 3.221490868073959e+294 < (/ (* x (- y z)) y)

    1. Initial program 58.8

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

    3. Applied associate-/l*1.3

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

    5. Applied clear-num1.4

      \[\leadsto \color{blue}{\frac{1}{\frac{\frac{y}{y - z}}{x}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -5.271300469497502 \cdot 10^{69}:\\ \;\;\;\;\frac{x}{y} \cdot \left(y - z\right)\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.55259092160079069 \cdot 10^{-42}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \le 3.22149086807395917 \cdot 10^{294}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020126 
(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))