Average Error: 12.5 → 3.0
Time: 2.7s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3.0580819637715248 \cdot 10^{-172} \lor \neg \left(y \le 1.26049536773617135 \cdot 10^{-263}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3.0580819637715248 \cdot 10^{-172} \lor \neg \left(y \le 1.26049536773617135 \cdot 10^{-263}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\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 <= -3.058081963771525e-172) || !(y <= 1.2604953677361714e-263))) {
		VAR = ((double) (x / ((double) (y / ((double) (y - z))))));
	} else {
		VAR = ((double) (1.0 / ((double) (y / ((double) (x * ((double) (y - z))))))));
	}
	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
Target3.1
Herbie3.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.0580819637715248e-172 or 1.26049536773617135e-263 < y

    1. Initial program 12.6

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

    3. Applied associate-/l*2.1

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

    if -3.0580819637715248e-172 < y < 1.26049536773617135e-263

    1. Initial program 11.2

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

    3. Applied clear-num11.3

      \[\leadsto \color{blue}{\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification3.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3.0580819637715248 \cdot 10^{-172} \lor \neg \left(y \le 1.26049536773617135 \cdot 10^{-263}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020175 
(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))