Average Error: 3.6 → 0.4
Time: 9.3s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -6.25037762144038382 \cdot 10^{116}:\\ \;\;\;\;1 \cdot x + z \cdot \left(\left(y - 1\right) \cdot x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \le 2.2478684520799233 \cdot 10^{172}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y - 1\right) + x \cdot 1\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \le -6.25037762144038382 \cdot 10^{116}:\\
\;\;\;\;1 \cdot x + z \cdot \left(\left(y - 1\right) \cdot x\right)\\

\mathbf{elif}\;\left(1 - y\right) \cdot z \le 2.2478684520799233 \cdot 10^{172}:\\
\;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\

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

\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 ((((double) (((double) (1.0 - y)) * z)) <= -6.250377621440384e+116)) {
		VAR = ((double) (((double) (1.0 * x)) + ((double) (z * ((double) (((double) (y - 1.0)) * x))))));
	} else {
		double VAR_1;
		if ((((double) (((double) (1.0 - y)) * z)) <= 2.2478684520799233e+172)) {
			VAR_1 = ((double) (x * ((double) (1.0 - ((double) (((double) (1.0 - y)) * z))))));
		} else {
			VAR_1 = ((double) (((double) (((double) (x * z)) * ((double) (y - 1.0)))) + ((double) (x * 1.0))));
		}
		VAR = VAR_1;
	}
	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

Original3.6
Target0.3
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (- 1.0 y) z) < -6.25037762144038382e116

    1. Initial program 11.1

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

    3. Applied sub-neg11.1

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

    4. Applied distribute-lft-in11.1

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

    5. Simplified11.1

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

    6. Simplified1.4

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

    if -6.25037762144038382e116 < (* (- 1.0 y) z) < 2.2478684520799233e172

    1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]

    if 2.2478684520799233e172 < (* (- 1.0 y) z)

    1. Initial program 15.6

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]

    2. Taylor expanded around inf 15.6

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

    3. Simplified0.8

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \le -6.25037762144038382 \cdot 10^{116}:\\ \;\;\;\;1 \cdot x + z \cdot \left(\left(y - 1\right) \cdot x\right)\\ \mathbf{elif}\;\left(1 - y\right) \cdot z \le 2.2478684520799233 \cdot 10^{172}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot z\right) \cdot \left(y - 1\right) + x \cdot 1\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))))