Average Error: 12.2 → 2.0
Time: 3.0s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y} \]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -4.722883590452615 \cdot 10^{+65} \lor \neg \left(y \leq 5.036863095834079 \cdot 10^{-170}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array} \]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -4.722883590452615 \cdot 10^{+65} \lor \neg \left(y \leq 5.036863095834079 \cdot 10^{-170}\right):\\
\;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\

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


\end{array}

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -4.722883590452615e+65) (not (<= y 5.036863095834079e-170)))
   (* x (- 1.0 (/ z y)))
   (- x (/ (* x z) y))))
double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((y <= -4.722883590452615e+65) || !(y <= 5.036863095834079e-170)) {
		tmp = x * (1.0 - (z / y));
	} else {
		tmp = x - ((x * z) / y);
	}
	return tmp;
}

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

Original12.2
Target2.9
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if y < -4.72288359045261534e65 or 5.0368630958340786e-170 < y

    1. Initial program 15.2

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

    2. Applied associate-/l*_binary640.9

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

    3. Applied div-inv_binary641.1

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

    4. Simplified1.0

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

    if -4.72288359045261534e65 < y < 5.0368630958340786e-170

    1. Initial program 7.0

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

    2. Taylor expanded in y around 0 3.7

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.722883590452615 \cdot 10^{+65} \lor \neg \left(y \leq 5.036863095834079 \cdot 10^{-170}\right):\\ \;\;\;\;x \cdot \left(1 - \frac{z}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \end{array} \]

Reproduce

herbie shell --seed 2021329 
(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))