Average Error: 10.2 → 0.3
Time: 2.8s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -4.03046809840641192 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(\left(y + 1\right) \cdot \frac{1}{z}\right) - x\\ \mathbf{elif}\;z \le 3.25448352394992233 \cdot 10^{-72}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + 1}{z} - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -4.03046809840641192 \cdot 10^{-54}:\\
\;\;\;\;x \cdot \left(\left(y + 1\right) \cdot \frac{1}{z}\right) - x\\

\mathbf{elif}\;z \le 3.25448352394992233 \cdot 10^{-72}:\\
\;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\

\mathbf{else}:\\
\;\;\;\;x \cdot \frac{y + 1}{z} - x\\

\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 <= -4.030468098406412e-54)) {
		VAR = ((double) (((double) (x * ((double) (((double) (y + 1.0)) * ((double) (1.0 / z)))))) - x));
	} else {
		double VAR_1;
		if ((z <= 3.2544835239499223e-72)) {
			VAR_1 = ((double) (((double) (x * ((double) (1.0 + ((double) (y - z)))))) / z));
		} else {
			VAR_1 = ((double) (((double) (x * ((double) (((double) (y + 1.0)) / z)))) - x));
		}
		VAR = VAR_1;
	}
	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

Original10.2
Target0.5
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -4.03046809840641192e-54

    1. Initial program 15.3

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

    2. Simplified0.4

      \[\leadsto \color{blue}{x \cdot \frac{y + 1}{z} - x}\]
    3. Using strategy rm

    4. Applied div-inv0.4

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

    if -4.03046809840641192e-54 < z < 3.25448352394992233e-72

    1. Initial program 0.1

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

    if 3.25448352394992233e-72 < z

    1. Initial program 13.4

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

    2. Simplified0.5

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -4.03046809840641192 \cdot 10^{-54}:\\ \;\;\;\;x \cdot \left(\left(y + 1\right) \cdot \frac{1}{z}\right) - x\\ \mathbf{elif}\;z \le 3.25448352394992233 \cdot 10^{-72}:\\ \;\;\;\;\frac{x \cdot \left(1 + \left(y - z\right)\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y + 1}{z} - x\\ \end{array}\]

Reproduce

herbie shell --seed 2020184 
(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))