Average Error: 3.7 → 0.2
Time: 2.9s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -1.0131972330345411 \cdot 10^{+58} \lor \neg \left(z \leq 1.0557290194481707 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot 1 + \left(z \cdot x\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \leq -1.0131972330345411 \cdot 10^{+58} \lor \neg \left(z \leq 1.0557290194481707 \cdot 10^{-24}\right):\\
\;\;\;\;x \cdot 1 + \left(z \cdot x\right) \cdot \left(y - 1\right)\\

\mathbf{else}:\\
\;\;\;\;x \cdot 1 + 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 -1.0131972330345411e+58) (not (<= z 1.0557290194481707e-24)))
   (+ (* x 1.0) (* (* z x) (- y 1.0)))
   (+ (* x 1.0) (* x (* z (- y 1.0))))))
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 (((z <= -1.0131972330345411e+58) || !(z <= 1.0557290194481707e-24))) {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (((double) (z * x)) * ((double) (y - 1.0))))));
	} else {
		VAR = ((double) (((double) (x * 1.0)) + ((double) (x * ((double) (z * ((double) (y - 1.0))))))));
	}
	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

Original3.7
Target0.3
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.013197233034541e58 or 1.0557290194481707e-24 < z

    1. Initial program 9.6

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

    3. Applied sub-neg9.6

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

    4. Applied distribute-lft-in9.6

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

    5. Simplified9.6

      \[\leadsto x \cdot 1 + \color{blue}{x \cdot \left(z \cdot \left(y - 1\right)\right)}\]
    6. Using strategy rm

    7. Applied associate-*r*0.1

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

    if -1.013197233034541e58 < z < 1.0557290194481707e-24

    1. Initial program 0.2

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

    3. Applied sub-neg0.2

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

    4. Applied distribute-lft-in0.2

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

    5. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.0131972330345411 \cdot 10^{+58} \lor \neg \left(z \leq 1.0557290194481707 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot 1 + \left(z \cdot x\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot 1 + x \cdot \left(z \cdot \left(y - 1\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020198 
(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))))