Average Error: 12.6 → 2.8
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -3.768692521689939 \cdot 10^{-195} \lor \neg \left(y \leq 2.116533356902775 \cdot 10^{-285}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -3.768692521689939 \cdot 10^{-195} \lor \neg \left(y \leq 2.116533356902775 \cdot 10^{-285}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.768692521689939e-195) (not (<= y 2.116533356902775e-285)))
   (/ x (/ y (- y z)))
   (/ 1.0 (/ y (* x (- y z))))))
double code(double x, double y, double z) {
	return (((double) (x * ((double) (y - z)))) / y);
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (((y <= -3.768692521689939e-195) || !(y <= 2.116533356902775e-285))) {
		tmp = (x / (y / ((double) (y - z))));
	} else {
		tmp = (1.0 / (y / ((double) (x * ((double) (y - z))))));
	}
	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

Original12.6
Target3.0
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.7686925216899389e-195 or 2.1165333569027749e-285 < y

    1. Initial program 12.7

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

    3. Applied associate-/l*_binary642.1

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

    if -3.7686925216899389e-195 < y < 2.1165333569027749e-285

    1. Initial program 11.2

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

    3. Applied clear-num_binary6411.2

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

  4. Final simplification2.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.768692521689939 \cdot 10^{-195} \lor \neg \left(y \leq 2.116533356902775 \cdot 10^{-285}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{y}{x \cdot \left(y - z\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020205 
(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))