Average Error: 3.4 → 0.1
Time: 2.7s
Precision: binary64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -5.299420080660153 \cdot 10^{-49} \lor \neg \left(z \leq 0.00011004603446563778\right):\\ \;\;\;\;x + \left(z \cdot x\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y - z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;z \leq -5.299420080660153 \cdot 10^{-49} \lor \neg \left(z \leq 0.00011004603446563778\right):\\
\;\;\;\;x + \left(z \cdot x\right) \cdot \left(y - 1\right)\\

\mathbf{else}:\\
\;\;\;\;x + x \cdot \left(z \cdot y - z\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 -5.299420080660153e-49) (not (<= z 0.00011004603446563778)))
   (+ x (* (* z x) (- y 1.0)))
   (+ x (* x (- (* z y) 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 ((z <= -5.299420080660153e-49) || !(z <= 0.00011004603446563778)) {
		tmp = x + ((z * x) * (y - 1.0));
	} else {
		tmp = x + (x * ((z * y) - 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
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -5.299420080660153e-49 or 1.10046034465637778e-4 < z

    1. Initial program 7.6

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

    3. Applied sub-neg_binary647.6

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

    4. Applied distribute-lft-in_binary647.6

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

    5. Simplified7.6

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

    6. Simplified7.6

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

    8. Applied *-un-lft-identity_binary647.6

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

    9. Applied distribute-rgt-out--_binary647.6

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

    10. Applied associate-*r*_binary640.2

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

    if -5.299420080660153e-49 < z < 1.10046034465637778e-4

    1. Initial program 0.1

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

    3. Applied sub-neg_binary640.1

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

    4. Applied distribute-lft-in_binary640.1

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

    5. Simplified0.1

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

    6. Simplified0.1

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

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.299420080660153 \cdot 10^{-49} \lor \neg \left(z \leq 0.00011004603446563778\right):\\ \;\;\;\;x + \left(z \cdot x\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot y - z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020231 
(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))))