Average Error: 3.3 → 0.4
Time: 3.1s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.49884295671476 \cdot 10^{+112} \lor \neg \left(z \leq 1.4089650473537223 \cdot 10^{+68}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \end{array} \]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.49884295671476 \cdot 10^{+112} \lor \neg \left(z \leq 1.4089650473537223 \cdot 10^{+68}\right):\\
\;\;\;\;x + z \cdot \left(x \cdot \left(y - 1\right)\right)\\

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


\end{array}

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))
↓
(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.49884295671476e+112) (not (<= z 1.4089650473537223e+68)))
   (+ x (* z (* x (- y 1.0))))
   (+ x (* x (* z (- y 1.0))))))
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 ((z <= -1.49884295671476e+112) || !(z <= 1.4089650473537223e+68)) {
		tmp = x + (z * (x * (y - 1.0)));
	} else {
		tmp = x + (x * (z * (y - 1.0)));
	}
	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

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

Derivation

  1. Split input into 2 regimes

  2. if z < -1.49884295671476e112 or 1.4089650473537223e68 < z

    1. Initial program 12.3

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

    2. Applied sub-neg_binary6412.3

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

    3. Applied distribute-rgt-in_binary6412.3

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

    4. Simplified12.3

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

    5. Simplified0.1

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

    6. Taylor expanded in x around inf 0.1

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

    if -1.49884295671476e112 < z < 1.4089650473537223e68

    1. Initial program 0.5

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

    2. Applied sub-neg_binary640.5

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

    3. Applied distribute-rgt-in_binary640.5

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.49884295671476 \cdot 10^{+112} \lor \neg \left(z \leq 1.4089650473537223 \cdot 10^{+68}\right):\\ \;\;\;\;x + z \cdot \left(x \cdot \left(y - 1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \end{array} \]

Reproduce

herbie shell --seed 2021313 
(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))))