Average Error: 3.5 → 0.5
Time: 22.7s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -0.6671287443065765:\\ \;\;\;\;\left(x + x \cdot \left(z \cdot y\right)\right) - x \cdot z\\ \mathbf{elif}\;x \leq 5.387746339016036 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z \cdot y + 1\right) - z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;x \leq -0.6671287443065765:\\
\;\;\;\;\left(x + x \cdot \left(z \cdot y\right)\right) - x \cdot z\\

\mathbf{elif}\;x \leq 5.387746339016036 \cdot 10^{-122}:\\
\;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\

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

\end{array}
(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))
↓
(FPCore (x y z)
 :precision binary64
 (if (<= x -0.6671287443065765)
   (- (+ x (* x (* z y))) (* x z))
   (if (<= x 5.387746339016036e-122)
     (+ x (* z (- (* x y) x)))
     (* x (- (+ (* z y) 1.0) z)))))
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 (x <= -0.6671287443065765) {
		tmp = (x + (x * (z * y))) - (x * z);
	} else if (x <= 5.387746339016036e-122) {
		tmp = x + (z * ((x * y) - x));
	} else {
		tmp = x * (((z * y) + 1.0) - z);
	}
	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

Original3.5
Target0.2
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -0.66712874430657654

    1. Initial program 0.1

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

    2. Taylor expanded around 0 0.1

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

    if -0.66712874430657654 < x < 5.3877463390160363e-122

    1. Initial program 6.3

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

    3. Applied sub-neg_binary64_201906.3

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

    4. Applied distribute-rgt-in_binary64_201476.3

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

    5. Simplified6.3

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

    6. Simplified6.3

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

    7. Taylor expanded around 0 0.1

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

    if 5.3877463390160363e-122 < x

    1. Initial program 1.3

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

    2. Taylor expanded around 0 1.3

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

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.6671287443065765:\\ \;\;\;\;\left(x + x \cdot \left(z \cdot y\right)\right) - x \cdot z\\ \mathbf{elif}\;x \leq 5.387746339016036 \cdot 10^{-122}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\left(z \cdot y + 1\right) - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021090 
(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))))