Average Error: 13.1 → 1.5
Time: 7.4s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2.512127525801556 \cdot 10^{-111}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2.512127525801556 \cdot 10^{-111}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (- y z)) y) (- INFINITY))
   (* x (/ (- y z) y))
   (if (<= (/ (* x (- y z)) y) -2.512127525801556e-111)
     (- x (/ (* x z) y))
     (/ x (/ y (- y z))))))
double code(double x, double y, double z) {
	return (x * (y - z)) / y;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if (((x * (y - z)) / y) <= -((double) INFINITY)) {
		tmp = x * ((y - z) / y);
	} else if (((x * (y - z)) / y) <= -2.512127525801556e-111) {
		tmp = x - ((x * z) / y);
	} else {
		tmp = x / (y / (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

Original13.1
Target2.9
Herbie1.5
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0

    1. Initial program 64.0

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

    3. Applied *-un-lft-identity_binary64_2360764.0

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

    4. Applied times-frac_binary64_236130.1

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

    5. Simplified0.1

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

    if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -2.5121275258015562e-111

    1. Initial program 0.4

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

    3. Applied associate-/l*_binary64_235525.8

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

    4. Taylor expanded around 0 0.3

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

    if -2.5121275258015562e-111 < (/.f64 (*.f64 x (-.f64 y z)) y)

    1. Initial program 12.6

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

    3. Applied associate-/l*_binary64_235522.2

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

  4. Final simplification1.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -2.512127525801556 \cdot 10^{-111}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021023 
(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))