Average Error: 12.6 → 0.3
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1.4224351408254982 \cdot 10^{+39}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 4.903639599729731 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5.366252742301081 \cdot 10^{+289}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1.4224351408254982 \cdot 10^{+39}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 4.903639599729731 \cdot 10^{-21}:\\
\;\;\;\;x \cdot \frac{y - z}{y}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5.366252742301081 \cdot 10^{+289}:\\
\;\;\;\;\frac{x \cdot \left(y - z\right)}{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 (- y z)))
   (if (<= (/ (* x (- y z)) y) -1.4224351408254982e+39)
     (/ (* x (- y z)) y)
     (if (<= (/ (* x (- y z)) y) 4.903639599729731e-21)
       (* x (/ (- y z) y))
       (if (<= (/ (* x (- y z)) y) 5.366252742301081e+289)
         (/ (* x (- y 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 / (y - z));
	} else if (((x * (y - z)) / y) <= -1.4224351408254982e+39) {
		tmp = (x * (y - z)) / y;
	} else if (((x * (y - z)) / y) <= 4.903639599729731e-21) {
		tmp = x * ((y - z) / y);
	} else if (((x * (y - z)) / y) <= 5.366252742301081e+289) {
		tmp = (x * (y - 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

Original12.6
Target3.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x (-.f64 y z)) y) < -inf.0 or 5.36625274230108079e289 < (/.f64 (*.f64 x (-.f64 y z)) y)

    1. Initial program 60.6

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

    3. Applied associate-/l*_binary64_170730.8

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

    if -inf.0 < (/.f64 (*.f64 x (-.f64 y z)) y) < -1.42243514082549816e39 or 4.90363959972973067e-21 < (/.f64 (*.f64 x (-.f64 y z)) y) < 5.36625274230108079e289

    1. Initial program 0.2

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

    if -1.42243514082549816e39 < (/.f64 (*.f64 x (-.f64 y z)) y) < 4.90363959972973067e-21

    1. Initial program 6.5

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

    3. Applied *-un-lft-identity_binary64_171286.5

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

    4. Applied times-frac_binary64_171340.2

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

    5. Simplified0.2

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq -\infty:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq -1.4224351408254982 \cdot 10^{+39}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 4.903639599729731 \cdot 10^{-21}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 5.366252742301081 \cdot 10^{+289}:\\ \;\;\;\;\frac{x \cdot \left(y - z\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020344 
(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))