Average Error: 3.3 → 0.3
Time: 3.7s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.4004148216332521 \cdot 10^{-37} \lor \neg \left(z \le 1.29604611734931964 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\sqrt[3]{1 - \left(1 - y\right) \cdot z} \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\right)\right) \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.4004148216332521 \cdot 10^{-37} \lor \neg \left(z \le 1.29604611734931964 \cdot 10^{-41}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(\sqrt[3]{1 - \left(1 - y\right) \cdot z} \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\right)\right) \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (x * ((double) (1.0 - ((double) (((double) (1.0 - y)) * z))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((z <= -1.400414821633252e-37) || !(z <= 1.2960461173493196e-41))) {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (((double) (x * z)) * ((double) (y - 1.0))))));
	} else {
		VAR = ((double) (((double) (x * ((double) (((double) cbrt(((double) (1.0 - ((double) (((double) (1.0 - y)) * z)))))) * ((double) cbrt(((double) (1.0 - ((double) (((double) (1.0 - y)) * z)))))))))) * ((double) cbrt(((double) (1.0 - ((double) (((double) (1.0 - y)) * 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

Original3.3
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.4004148216332521e-37 or 1.29604611734931964e-41 < z

    1. Initial program 7.1

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

    3. Applied sub-neg7.1

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

    4. Applied distribute-lft-in7.1

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

    5. Simplified0.2

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

    if -1.4004148216332521e-37 < z < 1.29604611734931964e-41

    1. Initial program 0.1

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

    3. Applied add-cube-cbrt0.3

      \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{1 - \left(1 - y\right) \cdot z} \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\right) \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\right)}\]

    4. Applied associate-*r*0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.4004148216332521 \cdot 10^{-37} \lor \neg \left(z \le 1.29604611734931964 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(\sqrt[3]{1 - \left(1 - y\right) \cdot z} \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\right)\right) \cdot \sqrt[3]{1 - \left(1 - y\right) \cdot z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020161 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (neg z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (neg z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))