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 r776026 = x;
        double r776027 = 1.0;
        double r776028 = y;
        double r776029 = r776027 - r776028;
        double r776030 = z;
        double r776031 = r776029 * r776030;
        double r776032 = r776027 - r776031;
        double r776033 = r776026 * r776032;
        return r776033;
}
↓
double f(double x, double y, double z) {
        double r776034 = x;
        double r776035 = 1.0;
        double r776036 = y;
        double r776037 = r776035 - r776036;
        double r776038 = z;
        double r776039 = r776037 * r776038;
        double r776040 = r776035 - r776039;
        double r776041 = r776034 * r776040;
        double r776042 = -inf.0;
        bool r776043 = r776041 <= r776042;
        double r776044 = 9.731870872043227e+191;
        bool r776045 = r776041 <= r776044;
        double r776046 = !r776045;
        bool r776047 = r776043 || r776046;
        double r776048 = r776034 * r776035;
        double r776049 = r776034 * r776038;
        double r776050 = r776036 - r776035;
        double r776051 = r776049 * r776050;
        double r776052 = r776048 + r776051;
        double r776053 = r776047 ? r776052 : r776041;
        return r776053;
}

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))))