Average Error: 3.5 → 0.1
Time: 3.0s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) = -\infty \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 9.7318708720432269 \cdot 10^{191}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
\begin{array}{l}
\mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) = -\infty \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 9.7318708720432269 \cdot 10^{191}\right):\\
\;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\

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

\end{array}
double f(double x, double y, double z) {
        double r990169 = x;
        double r990170 = 1.0;
        double r990171 = y;
        double r990172 = r990170 - r990171;
        double r990173 = z;
        double r990174 = r990172 * r990173;
        double r990175 = r990170 - r990174;
        double r990176 = r990169 * r990175;
        return r990176;
}
↓
double f(double x, double y, double z) {
        double r990177 = x;
        double r990178 = 1.0;
        double r990179 = y;
        double r990180 = r990178 - r990179;
        double r990181 = z;
        double r990182 = r990180 * r990181;
        double r990183 = r990178 - r990182;
        double r990184 = r990177 * r990183;
        double r990185 = -inf.0;
        bool r990186 = r990184 <= r990185;
        double r990187 = 9.731870872043227e+191;
        bool r990188 = r990184 <= r990187;
        double r990189 = !r990188;
        bool r990190 = r990186 || r990189;
        double r990191 = r990177 * r990178;
        double r990192 = r990177 * r990181;
        double r990193 = r990179 - r990178;
        double r990194 = r990192 * r990193;
        double r990195 = r990191 + r990194;
        double r990196 = r990190 ? r990195 : r990184;
        return r990196;
}

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
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x (- 1.0 (* (- 1.0 y) z))) < -inf.0 or 9.731870872043227e+191 < (* x (- 1.0 (* (- 1.0 y) z)))

    1. Initial program 21.5

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

    3. Applied sub-neg21.5

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

    4. Applied distribute-lft-in21.5

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

    5. Simplified0.2

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

    if -inf.0 < (* x (- 1.0 (* (- 1.0 y) z))) < 9.731870872043227e+191

    1. Initial program 0.1

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) = -\infty \lor \neg \left(x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \le 9.7318708720432269 \cdot 10^{191}\right):\\ \;\;\;\;x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1 (* (- 1 y) z))) -1.618195973607049e+50) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x)))))

  (* x (- 1 (* (- 1 y) z))))