Average Error: 3.6 → 0.1
Time: 6.9s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 4.839780608482324 \cdot 10^{+217}\right):\\ \;\;\;\;x + z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + x \cdot \left(y \cdot z\right)\right) - z \cdot x\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 4.839780608482324 \cdot 10^{+217}\right):\\
\;\;\;\;x + z \cdot \left(y \cdot x - x\right)\\

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

\end{array}
(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= (* (- 1.0 y) z) (- INFINITY))
         (not (<= (* (- 1.0 y) z) 4.839780608482324e+217)))
   (+ x (* z (- (* y x) x)))
   (- (+ x (* x (* y z))) (* z x))))
double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}
↓
double code(double x, double y, double z) {
	double tmp;
	if ((((1.0 - y) * z) <= -((double) INFINITY)) || !(((1.0 - y) * z) <= 4.839780608482324e+217)) {
		tmp = x + (z * ((y * x) - x));
	} else {
		tmp = (x + (x * (y * z))) - (z * x);
	}
	return tmp;
}

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
Target0.2
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 (-.f64 1 y) z) < -inf.0 or 4.83978060848232386e217 < (*.f64 (-.f64 1 y) z)

    1. Initial program 32.8

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

    3. Applied sub-neg_binary64_2257732.8

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

    4. Applied distribute-rgt-in_binary64_2253432.8

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

    5. Simplified32.8

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

    6. Simplified32.8

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

    7. Taylor expanded around 0 0.4

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

    if -inf.0 < (*.f64 (-.f64 1 y) z) < 4.83978060848232386e217

    1. Initial program 0.1

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

    2. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(1 - y\right) \cdot z \leq -\infty \lor \neg \left(\left(1 - y\right) \cdot z \leq 4.839780608482324 \cdot 10^{+217}\right):\\ \;\;\;\;x + z \cdot \left(y \cdot x - x\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + x \cdot \left(y \cdot z\right)\right) - z \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2021093 
(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) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

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