Average Error: 10.6 → 0.3
Time: 3.5s
Precision: binary64
\[\frac{x + y \cdot \left(z - x\right)}{z}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.1547986762301652 \cdot 10^{+37} \lor \neg \left(z \leq 1.6128080895465512 \cdot 10^{+100}\right):\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y \cdot x}{z}\\ \end{array}\]
\frac{x + y \cdot \left(z - x\right)}{z}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.1547986762301652 \cdot 10^{+37} \lor \neg \left(z \leq 1.6128080895465512 \cdot 10^{+100}\right):\\
\;\;\;\;y + x \cdot \frac{1 - y}{z}\\

\mathbf{else}:\\
\;\;\;\;y + \frac{x - y \cdot x}{z}\\

\end{array}
double code(double x, double y, double z) {
	return (((double) (x + ((double) (y * ((double) (z - x)))))) / z);
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.1547986762301652e+37) || !(z <= 1.6128080895465512e+100))) {
		VAR = ((double) (y + ((double) (x * (((double) (1.0 - y)) / z)))));
	} else {
		VAR = ((double) (y + (((double) (x - ((double) (y * 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

Original10.6
Target0.0
Herbie0.3
\[\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.15479867623016523e37 or 1.6128080895465512e100 < z

    1. Initial program 20.1

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

    2. Simplified0.1

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

    if -1.15479867623016523e37 < z < 1.6128080895465512e100

    1. Initial program 1.4

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

    2. Simplified6.7

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

    4. Applied associate-*r/0.5

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

    5. Simplified0.5

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1547986762301652 \cdot 10^{+37} \lor \neg \left(z \leq 1.6128080895465512 \cdot 10^{+100}\right):\\ \;\;\;\;y + x \cdot \frac{1 - y}{z}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020199 
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
  :precision binary64

  :herbie-target
  (- (+ y (/ x z)) (/ y (/ z x)))

  (/ (+ x (* y (- z x))) z))