Average Error: 10.2 → 0.6
Time: 2.9s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -8.3294717432622867 \cdot 10^{148} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 43365737702639354000\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -8.3294717432622867 \cdot 10^{148} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 43365737702639354000\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\

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

\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 (((((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z)) <= -8.329471743262287e+148) || !(((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z)) <= 4.336573770263935e+19))) {
		VAR = ((double) (((double) (((double) (x / z)) * ((double) (y + 1.0)))) - x));
	} else {
		VAR = ((double) (x / ((double) (z / ((double) (((double) (y - z)) + 1.0))))));
	}
	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
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -8.3294717432622867e148 or 43365737702639354000 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 21.8

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

    2. Simplified5.6

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

    4. Applied clear-num5.6

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

    6. Applied associate-/r/5.6

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

    7. Applied associate-*r*0.2

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

    8. Simplified0.1

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

    if -8.3294717432622867e148 < (/ (* x (+ (- y z) 1.0)) z) < 43365737702639354000

    1. Initial program 0.1

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

    3. Applied associate-/l*1.1

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -8.3294717432622867 \cdot 10^{148} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 43365737702639354000\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(y + 1\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))