Average Error: 10.2 → 0.5
Time: 11.2s
Precision: binary64
\[\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -2.0770626203723886 \cdot 10^{118} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 3.47616615834701316 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]
\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 -2.0770626203723886 \cdot 10^{118} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 3.47616615834701316 \cdot 10^{-108}\right):\\
\;\;\;\;\frac{x}{z} \cdot \left(1 + y\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)) <= -2.0770626203723886e+118) || !(((double) (((double) (x * ((double) (((double) (y - z)) + 1.0)))) / z)) <= 3.476166158347013e-108))) {
		VAR = ((double) (((double) (((double) (x / z)) * ((double) (1.0 + y)))) - 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
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \lt -2.7148310671343599 \cdot 10^{-162}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \mathbf{elif}\;x \lt 3.87410881643954616 \cdot 10^{-197}:\\ \;\;\;\;\left(x \cdot \left(\left(y - z\right) + 1\right)\right) \cdot \frac{1}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(1 + y\right) \cdot \frac{x}{z} - x\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (/ (* x (+ (- y z) 1.0)) z) < -2.0770626203723886e118 or 3.47616615834701316e-108 < (/ (* x (+ (- y z) 1.0)) z)

    1. Initial program 17.0

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

    3. Applied associate-/l*4.9

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

    5. Applied associate-/r/1.4

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

    6. Taylor expanded around 0 5.5

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

    7. Simplified0.4

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

    if -2.0770626203723886e118 < (/ (* x (+ (- y z) 1.0)) z) < 3.47616615834701316e-108

    1. Initial program 0.1

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

    3. Applied associate-/l*0.6

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le -2.0770626203723886 \cdot 10^{118} \lor \neg \left(\frac{x \cdot \left(\left(y - z\right) + 1\right)}{z} \le 3.47616615834701316 \cdot 10^{-108}\right):\\ \;\;\;\;\frac{x}{z} \cdot \left(1 + y\right) - x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\left(y - z\right) + 1}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(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))