Average Error: 3.4 → 0.3
Time: 6.0s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -8.860384044370192 \cdot 10^{+89}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;x \leq 3.5093842705709426 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;x \leq -8.860384044370192 \cdot 10^{+89}:\\
\;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\

\mathbf{elif}\;x \leq 3.5093842705709426 \cdot 10^{-44}:\\
\;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\

\mathbf{else}:\\
\;\;\;\;x + x \cdot \left(y \cdot z - 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 -8.860384044370192e+89)
   (+ x (* x (* z (+ y -1.0))))
   (if (<= x 3.5093842705709426e-44)
     (+ x (* z (- (* x y) x)))
     (+ x (* x (- (* y z) 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 <= -8.860384044370192e+89) {
		tmp = x + (x * (z * (y + -1.0)));
	} else if (x <= 3.5093842705709426e-44) {
		tmp = x + (z * ((x * y) - x));
	} else {
		tmp = x + (x * ((y * z) - 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

Original3.4
Target0.2
Herbie0.3
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if x < -8.8603840443701918e89

    1. Initial program 0.1

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

    3. Applied sub-neg_binary64_229180.1

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

    4. Applied distribute-rgt-in_binary64_228750.1

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

    if -8.8603840443701918e89 < x < 3.50938427057094256e-44

    1. Initial program 5.2

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

    3. Applied sub-neg_binary64_229185.2

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

    4. Applied distribute-rgt-in_binary64_228755.2

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

    5. Simplified5.2

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

    6. Simplified5.2

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

    7. Taylor expanded around 0 0.3

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

    if 3.50938427057094256e-44 < x

    1. Initial program 0.3

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

    3. Applied sub-neg_binary64_229180.3

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

    4. Applied distribute-rgt-in_binary64_228750.3

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

    5. Simplified0.3

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

    6. Simplified0.3

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

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.860384044370192 \cdot 10^{+89}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;x \leq 3.5093842705709426 \cdot 10^{-44}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(y \cdot z - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2021014 
(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))))