Average Error: 10.8 → 0.2
Time: 14.2s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -4.69841935672323576 \cdot 10^{-129} \lor \neg \left(x \le 108237781843921616\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x + 1 \cdot x}{z}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;x \le -4.69841935672323576 \cdot 10^{-129} \lor \neg \left(x \le 108237781843921616\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\

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

\end{array}
double code(double x, double y, double z) {
	return (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((x <= -4.698419356723236e-129) || !(x <= 1.0823778184392162e+17))) {
		VAR = ((double) (((double) ((x / z) * ((double) (1.0 + y)))) - x));
	} else {
		VAR = (((double) (((double) (((double) (y - z)) * x)) + ((double) (1.0 * x)))) / 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

Original10.8
Target0.5
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 x < -4.69841935672323576e-129 or 108237781843921616 < x

    1. Initial program 21.2

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

    2. Taylor expanded around 0 7.1

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

    3. Simplified0.2

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

    if -4.69841935672323576e-129 < x < 108237781843921616

    1. Initial program 0.2

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

    3. Applied distribute-lft-in0.2

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

    4. Simplified0.2

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

    5. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -4.69841935672323576 \cdot 10^{-129} \lor \neg \left(x \le 108237781843921616\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(y - z\right) \cdot x + 1 \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))