Average Error: 0.4 → 0.2
Time: 14.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)
double f(double x, double y, double z) {
        double r270603 = x;
        double r270604 = y;
        double r270605 = r270604 - r270603;
        double r270606 = 6.0;
        double r270607 = r270605 * r270606;
        double r270608 = 2.0;
        double r270609 = 3.0;
        double r270610 = r270608 / r270609;
        double r270611 = z;
        double r270612 = r270610 - r270611;
        double r270613 = r270607 * r270612;
        double r270614 = r270603 + r270613;
        return r270614;
}
↓
double f(double x, double y, double z) {
        double r270615 = x;
        double r270616 = y;
        double r270617 = r270616 - r270615;
        double r270618 = 4.0;
        double r270619 = 6.0;
        double r270620 = z;
        double r270621 = r270619 * r270620;
        double r270622 = r270618 - r270621;
        double r270623 = r270617 * r270622;
        double r270624 = r270615 + r270623;
        return r270624;
}

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. Taylor expanded around 0 0.2

    \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(4 - 6 \cdot z\right)}\]

  5. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(4 - 6 \cdot z\right)\]

Reproduce

herbie shell --seed 2019298 
(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))))