Average Error: 0.4 → 0.2
Time: 2.9s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)
double f(double x, double y, double z) {
        double r230121 = x;
        double r230122 = y;
        double r230123 = r230122 - r230121;
        double r230124 = 6.0;
        double r230125 = r230123 * r230124;
        double r230126 = 2.0;
        double r230127 = 3.0;
        double r230128 = r230126 / r230127;
        double r230129 = z;
        double r230130 = r230128 - r230129;
        double r230131 = r230125 * r230130;
        double r230132 = r230121 + r230131;
        return r230132;
}
↓
double f(double x, double y, double z) {
        double r230133 = x;
        double r230134 = y;
        double r230135 = r230134 - r230133;
        double r230136 = 2.0;
        double r230137 = 3.0;
        double r230138 = r230136 / r230137;
        double r230139 = 6.0;
        double r230140 = r230138 * r230139;
        double r230141 = r230135 * r230140;
        double r230142 = z;
        double r230143 = -r230142;
        double r230144 = r230143 * r230139;
        double r230145 = r230135 * r230144;
        double r230146 = r230141 + r230145;
        double r230147 = r230133 + r230146;
        return r230147;
}

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

Derivation

  1. Initial program 0.4

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)}\]
  4. Using strategy rm

  5. Applied sub-neg0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}\right)\]

  6. Applied distribute-lft-in0.2

    \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(6 \cdot \frac{2}{3} + 6 \cdot \left(-z\right)\right)}\]

  7. Applied distribute-lft-in0.2

    \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \frac{2}{3}\right) + \left(y - x\right) \cdot \left(6 \cdot \left(-z\right)\right)\right)}\]

  8. Simplified0.2

    \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right)} + \left(y - x\right) \cdot \left(6 \cdot \left(-z\right)\right)\right)\]

  9. Simplified0.2

    \[\leadsto x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \color{blue}{\left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)}\right)\]

  10. Final simplification0.2

    \[\leadsto x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)\]

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6) (- (/ 2 3) z))))