Average Error: 12.6 → 1.7
Time: 4.1s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.337823436972603 \cdot 10^{-24} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 8.81099014379826153 \cdot 10^{295}\right):\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.337823436972603 \cdot 10^{-24} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 8.81099014379826153 \cdot 10^{295}\right):\\
\;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\

\mathbf{else}:\\
\;\;\;\;x - \frac{x \cdot z}{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)) <= 2.337823436972603e-24) || !(((double) (((double) (x * ((double) (y - z)))) / y)) <= 8.810990143798262e+295))) {
		VAR = ((double) (1.0 / ((double) (((double) (y / ((double) (y - z)))) / x))));
	} else {
		VAR = ((double) (x - ((double) (((double) (x * 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

Original12.6
Target3.0
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt -2.060202331921739 \cdot 10^{104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z \lt 1.69397660138285259 \cdot 10^{213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (- y z)) y) < 2.337823436972603e-24 or 8.81099014379826153e295 < (/ (* x (- y z)) y)

    1. Initial program 16.4

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

    3. Applied associate-/l*2.0

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

    5. Applied clear-num2.2

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

    if 2.337823436972603e-24 < (/ (* x (- y z)) y) < 8.81099014379826153e295

    1. Initial program 0.2

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

    3. Applied associate-/l*5.5

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

    4. Taylor expanded around 0 0.2

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

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \le 2.337823436972603 \cdot 10^{-24} \lor \neg \left(\frac{x \cdot \left(y - z\right)}{y} \le 8.81099014379826153 \cdot 10^{295}\right):\\ \;\;\;\;\frac{1}{\frac{\frac{y}{y - z}}{x}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array}\]

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))