Average Error: 12.3 → 2.6
Time: 4.7s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y} \]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -1.3984342212002436 \cdot 10^{-55} \lor \neg \left(y \leq 1.5271497062397503 \cdot 10^{-199}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{y - z}{\sqrt[3]{y}}\\ \end{array} \]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -1.3984342212002436 \cdot 10^{-55} \lor \neg \left(y \leq 1.5271497062397503 \cdot 10^{-199}\right):\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{else}:\\
\;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{y - z}{\sqrt[3]{y}}\\


\end{array}

(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.3984342212002436e-55) (not (<= y 1.5271497062397503e-199)))
   (/ x (/ y (- y z)))
   (* (/ x (* (cbrt y) (cbrt y))) (/ (- y z) (cbrt 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 <= -1.3984342212002436e-55) || !(y <= 1.5271497062397503e-199)) {
		tmp = x / (y / (y - z));
	} else {
		tmp = (x / (cbrt(y) * cbrt(y))) * ((y - z) / cbrt(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

Original12.3
Target3.2
Herbie2.6
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array} \]

Derivation

  1. Split input into 2 regimes

  2. if y < -1.39843422120024364e-55 or 1.52714970623975034e-199 < y

    1. Initial program 13.2

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

    2. Applied associate-/l*_binary641.0

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

    3. Applied *-un-lft-identity_binary641.0

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

    if -1.39843422120024364e-55 < y < 1.52714970623975034e-199

    1. Initial program 9.2

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

    2. Applied add-cube-cbrt_binary6410.2

      \[\leadsto \frac{x \cdot \left(y - z\right)}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \]

    3. Applied times-frac_binary648.4

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

  4. Final simplification2.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3984342212002436 \cdot 10^{-55} \lor \neg \left(y \leq 1.5271497062397503 \cdot 10^{-199}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{y - z}{\sqrt[3]{y}}\\ \end{array} \]

Reproduce

herbie shell --seed 2021275 
(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))