Average Error: 12.9 → 2.0
Time: 2.3s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.7699277626159894 \cdot 10^{303} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -8.94979025560652625 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.7699277626159894 \cdot 10^{303} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -8.94979025560652625 \cdot 10^{-52}\right):\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{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 (((((double) (((double) (x * ((double) (y - z)))) / y)) <= -1.7699277626159894e+303) || !(((double) (((double) (x * ((double) (y - z)))) / y)) <= -8.949790255606526e-52))) {
		VAR = ((double) (x * ((double) (((double) (y - z)) / y))));
	} else {
		VAR = ((double) (((double) (x * ((double) (y - 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

Original12.9
Target3.4
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < -1.7699277626159894e303 or -8.94979025560652625e-52 < (/ (* x (- y z)) y)

    1. Initial program 16.9

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

    3. Applied *-un-lft-identity16.9

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

    4. Applied times-frac2.5

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

    5. Simplified2.5

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

    if -1.7699277626159894e303 < (/ (* x (- y z)) y) < -8.94979025560652625e-52

    1. Initial program 0.3

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le -1.7699277626159894 \cdot 10^{303} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le -8.94979025560652625 \cdot 10^{-52}\right):\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(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))