Average Error: 9.5 → 0.1
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -4.017127125067015 \cdot 10^{+40} \lor \neg \left(z \leq 4.27404980573066 \cdot 10^{-06}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + \frac{x}{z}\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -4.017127125067015 \cdot 10^{+40} \lor \neg \left(z \leq 4.27404980573066 \cdot 10^{-06}\right):\\
\;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\

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

\end{array}
(FPCore (x y z) :precision binary64 (/ (* x (+ (- y z) 1.0)) z))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.017127125067015e+40) (not (<= z 4.27404980573066e-06)))
   (* x (/ (+ (- y z) 1.0) z))
   (- (+ (/ (* x y) z) (/ 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 <= -4.017127125067015e+40) || !(z <= 4.27404980573066e-06)) {
		tmp = x * (((y - z) + 1.0) / z);
	} else {
		tmp = (((x * y) / z) + (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

Original9.5
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 < -4.0171271250670149e40 or 4.27404980573066016e-6 < z

    1. Initial program 16.2

      \[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity_binary6416.2

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

    4. Applied times-frac_binary640.1

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

    5. Simplified0.1

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

    if -4.0171271250670149e40 < z < 4.27404980573066016e-6

    1. Initial program 0.3

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

    2. Taylor expanded around 0 0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.017127125067015 \cdot 10^{+40} \lor \neg \left(z \leq 4.27404980573066 \cdot 10^{-06}\right):\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + \frac{x}{z}\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2020220 
(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))