Average Error: 10.0 → 0.1
Time: 2.8s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -13140418048897928 \lor \neg \left(z \le 154467.80216557847\right):\\ \;\;\;\;\frac{x \cdot 1}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \le -13140418048897928 \lor \neg \left(z \le 154467.80216557847\right):\\
\;\;\;\;\frac{x \cdot 1}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{else}:\\
\;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{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 <= -13140418048897928.0) || !(z <= 154467.80216557847))) {
		temp = ((x * 1.0) / (z / ((y - z) + 1.0)));
	} else {
		temp = (((y - z) + 1.0) * (x / z));
	}
	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

Original10.0
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 2 regimes

  2. if z < -13140418048897928.0 or 154467.80216557847 < z

    1. Initial program 17.3

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

    3. Applied *-un-lft-identity17.3

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

    4. Applied associate-*r*17.3

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

    5. Applied associate-/l*0.1

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

    if -13140418048897928.0 < z < 154467.80216557847

    1. Initial program 0.2

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

    3. Applied *-un-lft-identity0.2

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

    4. Applied *-commutative0.2

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

    5. Applied times-frac0.2

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

    6. Simplified0.2

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -13140418048897928 \lor \neg \left(z \le 154467.80216557847\right):\\ \;\;\;\;\frac{x \cdot 1}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y - z\right) + 1\right) \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020066 +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))