Average Error: 12.1 → 2.9
Time: 7.5s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -5.350977060514043 \cdot 10^{-132} \lor \neg \left(y \leq 6.717350048078581 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{y - z}{\sqrt[3]{y}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -5.350977060514043 \cdot 10^{-132} \lor \neg \left(y \leq 6.717350048078581 \cdot 10^{-129}\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 -5.350977060514043e-132) (not (<= y 6.717350048078581e-129)))
   (/ 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 <= -5.350977060514043e-132) || !(y <= 6.717350048078581e-129)) {
		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

Original12.1
Target3.2
Herbie2.9
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.3509770605140432e-132 or 6.71735004807858134e-129 < y

    1. Initial program 12.8

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

    3. Applied associate-/l*_binary64_201420.9

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

    if -5.3509770605140432e-132 < y < 6.71735004807858134e-129

    1. Initial program 9.7

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

    3. Applied add-cube-cbrt_binary64_2023210.8

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

    4. Applied times-frac_binary64_2020310.0

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

  4. Final simplification2.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.350977060514043 \cdot 10^{-132} \lor \neg \left(y \leq 6.717350048078581 \cdot 10^{-129}\right):\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{y - z}{\sqrt[3]{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021027 
(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))