Average Error: 9.9 → 0.4
Time: 2.8s
Precision: 64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.7618411608635746 \cdot 10^{88}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 7.8501220882830768 \cdot 10^{-164}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -3.7618411608635746 \cdot 10^{88}:\\
\;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\

\mathbf{elif}\;x \le 7.8501220882830768 \cdot 10^{-164}:\\
\;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\

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

\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 ((x <= -3.7618411608635746e+88)) {
		temp = (x / (z / ((y - z) + 1.0)));
	} else {
		double temp_1;
		if ((x <= 7.850122088283077e-164)) {
			temp_1 = ((((x * y) / z) + (1.0 * (x / z))) - x);
		} else {
			temp_1 = (((x / z) * (1.0 + y)) - x);
		}
		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

Original9.9
Target0.6
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -3.7618411608635746e+88

    1. Initial program 35.3

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

    3. Applied associate-/l*0.1

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

    if -3.7618411608635746e+88 < x < 7.850122088283077e-164

    1. Initial program 1.3

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

    2. Taylor expanded around 0 0.5

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

    if 7.850122088283077e-164 < x

    1. Initial program 13.5

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

    2. Taylor expanded around 0 4.5

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

    3. Taylor expanded around 0 4.5

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

    4. Simplified0.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.7618411608635746 \cdot 10^{88}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \mathbf{elif}\;x \le 7.8501220882830768 \cdot 10^{-164}:\\ \;\;\;\;\left(\frac{x \cdot y}{z} + 1 \cdot \frac{x}{z}\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \end{array}\]

Reproduce

herbie shell --seed 2020053 
(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))