Average Error: 3.4 → 1.7
Time: 22.6s
Precision: 64
\[x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\]
↓
\[1 \cdot x + \left(x \cdot z\right) \cdot \left(y - 1\right)\]
x \cdot \left(1 - \left(1 - y\right) \cdot z\right)
↓
1 \cdot x + \left(x \cdot z\right) \cdot \left(y - 1\right)
double f(double x, double y, double z) {
        double r510663 = x;
        double r510664 = 1.0;
        double r510665 = y;
        double r510666 = r510664 - r510665;
        double r510667 = z;
        double r510668 = r510666 * r510667;
        double r510669 = r510664 - r510668;
        double r510670 = r510663 * r510669;
        return r510670;
}
↓
double f(double x, double y, double z) {
        double r510671 = 1.0;
        double r510672 = x;
        double r510673 = r510671 * r510672;
        double r510674 = z;
        double r510675 = r510672 * r510674;
        double r510676 = y;
        double r510677 = r510676 - r510671;
        double r510678 = r510675 * r510677;
        double r510679 = r510673 + r510678;
        return r510679;
}

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
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt -1.618195973607048970493874632750554853795 \cdot 10^{50}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{elif}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \lt 3.892237649663902900973248011051357504727 \cdot 10^{134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \end{array}\]

Derivation

  1. Initial program 3.4

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

  3. Applied sub-neg3.4

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

  4. Applied distribute-lft-in3.4

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

  5. Simplified3.4

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

  6. Simplified1.7

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

  7. Final simplification1.7

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

Reproduce

herbie shell --seed 2019306 
(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))) -1.618195973607049e50) (+ x (* (- 1 y) (* (- z) x))) (if (< (* x (- 1 (* (- 1 y) z))) 3.8922376496639029e134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1 y) (* (- z) x)))))

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