Average Error: 12.5 → 1.9
Time: 2.9s
Precision: binary64
\[\frac{x \cdot \left(y - z\right)}{y}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 8.399881127348085 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 3.830825279456158 \cdot 10^{+283}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]
\frac{x \cdot \left(y - z\right)}{y}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 8.399881127348085 \cdot 10^{-16}:\\
\;\;\;\;\frac{x}{\frac{y}{y - z}}\\

\mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 3.830825279456158 \cdot 10^{+283}:\\
\;\;\;\;x - \frac{x \cdot z}{y}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (- y z)) y))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= (/ (* x (- y z)) y) 8.399881127348085e-16)
   (/ x (/ y (- y z)))
   (if (<= (/ (* x (- y z)) y) 3.830825279456158e+283)
     (- x (/ (* x z) y))
     (* x (/ (- y z) 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 (((x * (y - z)) / y) <= 8.399881127348085e-16) {
		tmp = x / (y / (y - z));
	} else if (((x * (y - z)) / y) <= 3.830825279456158e+283) {
		tmp = x - ((x * z) / y);
	} else {
		tmp = x * ((y - z) / 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

Original12.5
Target3.2
Herbie1.9
\[\begin{array}{l} \mathbf{if}\;z < -2.060202331921739 \cdot 10^{+104}:\\ \;\;\;\;x - \frac{z \cdot x}{y}\\ \mathbf{elif}\;z < 1.6939766013828526 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{else}:\\ \;\;\;\;\left(y - z\right) \cdot \frac{x}{y}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/.f64 (*.f64 x (-.f64 y z)) y) < 8.39988112734808504e-16

    1. Initial program 10.8

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

    3. Applied sub-neg_binary6410.8

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

    4. Applied distribute-rgt-in_binary6410.8

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

    5. Simplified10.8

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

    6. Simplified10.8

      \[\leadsto \frac{x \cdot y + \color{blue}{\left(-x \cdot z\right)}}{y}\]
    7. Using strategy rm

    8. Applied distribute-rgt-neg-in_binary6410.8

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

    9. Applied distribute-lft-out_binary6410.8

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

    10. Applied associate-/l*_binary642.3

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

    if 8.39988112734808504e-16 < (/.f64 (*.f64 x (-.f64 y z)) y) < 3.83082527945615827e283

    1. Initial program 0.2

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

    2. Taylor expanded around 0 0.2

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

    if 3.83082527945615827e283 < (/.f64 (*.f64 x (-.f64 y z)) y)

    1. Initial program 54.9

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

    3. Applied *-un-lft-identity_binary6454.9

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

    4. Applied times-frac_binary642.5

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

  4. Final simplification1.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(y - z\right)}{y} \leq 8.399881127348085 \cdot 10^{-16}:\\ \;\;\;\;\frac{x}{\frac{y}{y - z}}\\ \mathbf{elif}\;\frac{x \cdot \left(y - z\right)}{y} \leq 3.830825279456158 \cdot 10^{+283}:\\ \;\;\;\;x - \frac{x \cdot z}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y - z}{y}\\ \end{array}\]

Alternatives

Reproduce

herbie shell --seed 2021118 
(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))