Average Error: 9.7 → 0.2
Time: 3.5s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -8.8460105965671407 \cdot 10^{37} \lor \neg \left(z \le 2.0854125815159318 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \frac{y + 1}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -8.8460105965671407 \cdot 10^{37} \lor \neg \left(z \le 2.0854125815159318 \cdot 10^{-10}\right):\\
\;\;\;\;x \cdot \frac{y + 1}{z} - x\\

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

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -8.84601059656714e+37) || !(z <= 2.0854125815159318e-10))) {
		VAR = ((double) (((double) (x * ((double) (((double) (y + 1.0)) / z)))) - x));
	} else {
		VAR = ((double) (((double) (x * ((double) (1.0 + ((double) (y - z)))))) / z));
	}
	return VAR;
}

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

Original9.7
Target0.6
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -8.8460105965671407e37 or 2.0854125815159318e-10 < z

    1. Initial program 16.7

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

    2. Simplified0.1

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

    if -8.8460105965671407e37 < z < 2.0854125815159318e-10

    1. Initial program 0.3

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -8.8460105965671407 \cdot 10^{37} \lor \neg \left(z \le 2.0854125815159318 \cdot 10^{-10}\right):\\ \;\;\;\;x \cdot \frac{y + 1}{z} - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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))