Average Error: 10.3 → 0.1
Time: 3.7s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -159.566156241908544:\\ \;\;\;\;\frac{x}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}\\ \mathbf{elif}\;z \le 8.26470253112780802 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{-z} \cdot \left(-\left(\left(y - z\right) + 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -159.566156241908544:\\
\;\;\;\;\frac{x}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}\\

\mathbf{elif}\;z \le 8.26470253112780802 \cdot 10^{-8}:\\
\;\;\;\;\frac{x}{-z} \cdot \left(-\left(\left(y - z\right) + 1\right)\right)\\

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

\end{array}
double code(double x, double y, double z) {
	return ((x * ((y - z) + 1.0)) / z);
}
↓
double code(double x, double y, double z) {
	double temp;
	if ((z <= -159.56615624190854)) {
		temp = (x / (-z / -((y - z) + 1.0)));
	} else {
		double temp_1;
		if ((z <= 8.264702531127808e-08)) {
			temp_1 = ((x / -z) * -((y - z) + 1.0));
		} else {
			temp_1 = (x * (((y - z) + 1.0) / z));
		}
		temp = temp_1;
	}
	return temp;
}

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
Target0.4
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if z < -159.56615624190854

    1. Initial program 17.1

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

    3. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied frac-2neg0.1

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

    if -159.56615624190854 < z < 8.264702531127808e-08

    1. Initial program 0.1

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

    3. Applied associate-/l*8.5

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{\left(y - z\right) + 1}}}\]
    4. Using strategy rm

    5. Applied frac-2neg8.5

      \[\leadsto \frac{x}{\color{blue}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}}\]
    6. Using strategy rm

    7. Applied associate-/r/0.1

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

    if 8.264702531127808e-08 < z

    1. Initial program 16.3

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

    3. Applied *-un-lft-identity16.3

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

    4. Applied times-frac0.1

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

    5. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -159.566156241908544:\\ \;\;\;\;\frac{x}{\frac{-z}{-\left(\left(y - z\right) + 1\right)}}\\ \mathbf{elif}\;z \le 8.26470253112780802 \cdot 10^{-8}:\\ \;\;\;\;\frac{x}{-z} \cdot \left(-\left(\left(y - z\right) + 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{\left(y - z\right) + 1}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(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 y) (/ x z)) x) (if (< x 3.874108816439546e-197) (* (* x (+ (- y z) 1)) (/ 1 z)) (- (* (+ 1 y) (/ x z)) x)))

  (/ (* x (+ (- y z) 1)) z))