Average Error: 10.3 → 0.1
Time: 9.5s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.4932932283986656 \cdot 10^{+36} \lor \neg \left(z \leq 3.425357687924926 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \frac{y + 1}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z} - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.4932932283986656 \cdot 10^{+36} \lor \neg \left(z \leq 3.425357687924926 \cdot 10^{-15}\right):\\
\;\;\;\;x \cdot \frac{y + 1}{z} - x\\

\mathbf{else}:\\
\;\;\;\;\left(y + 1\right) \cdot \frac{x}{z} - x\\

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.4932932283986656e+36) (not (<= z 3.425357687924926e-15)))
   (- (* x (/ (+ y 1.0) z)) x)
   (- (* (+ y 1.0) (/ x z)) x)))
double code(double x, double y, double z) {
	return (x * ((y - z) + 1.0)) / z;
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.4932932283986656e+36) || !(z <= 3.425357687924926e-15)) {
		tmp = (x * ((y + 1.0) / z)) - x;
	} else {
		tmp = ((y + 1.0) * (x / z)) - x;
	}
	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

Original10.3
Target0.5
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x < -2.71483106713436 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x < 3.874108816439546 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.49329322839866555e36 or 3.42535768792492597e-15 < z

    1. Initial program 17.4

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

    2. Simplified0.1

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

    if -1.49329322839866555e36 < z < 3.42535768792492597e-15

    1. Initial program 0.3

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

    2. Simplified0.3

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

    3. Taylor expanded around 0 0.2

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

    4. Simplified0.2

      \[\leadsto \color{blue}{\left(y + 1\right) \cdot \frac{x}{z}} - x\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4932932283986656 \cdot 10^{+36} \lor \neg \left(z \leq 3.425357687924926 \cdot 10^{-15}\right):\\ \;\;\;\;x \cdot \frac{y + 1}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\left(y + 1\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Reproduce

herbie shell --seed 2021176 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment.Bernstein:evaluateBernstein from diagrams-lib-1.3.0.3"
  :precision binary64

  :herbie-target
  (if (< x -2.71483106713436e-162) (- (* (+ 1.0 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1.0)) (/ 1.0 z)) (- (* (+ 1.0 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1.0)) z))