Average Error: 3.5 → 1.6
Time: 4.3s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
x \cdot 1 + \left(x \cdot z\right) \cdot \left(y - 1\right)
double f(double x, double y, double z) {
        double r852754 = x;
        double r852755 = 1.0;
        double r852756 = y;
        double r852757 = r852755 - r852756;
        double r852758 = z;
        double r852759 = r852757 * r852758;
        double r852760 = r852755 - r852759;
        double r852761 = r852754 * r852760;
        return r852761;
}
↓
double f(double x, double y, double z) {
        double r852762 = x;
        double r852763 = 1.0;
        double r852764 = r852762 * r852763;
        double r852765 = z;
        double r852766 = r852762 * r852765;
        double r852767 = y;
        double r852768 = r852767 - r852763;
        double r852769 = r852766 * r852768;
        double r852770 = r852764 + r852769;
        return r852770;
}

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
Target0.3
Herbie1.6
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607049 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.8922376496639029 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Initial program 3.5

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

  3. Applied sub-neg3.5

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

  4. Applied distribute-lft-in3.5

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

  5. Simplified1.6

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

  6. Final simplification1.6

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

Reproduce

herbie shell --seed 2020036 
(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))))