Average Error: 0.4 → 0.2
Time: 21.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)
double f(double x, double y, double z) {
        double r16763426 = x;
        double r16763427 = y;
        double r16763428 = r16763427 - r16763426;
        double r16763429 = 6.0;
        double r16763430 = r16763428 * r16763429;
        double r16763431 = 2.0;
        double r16763432 = 3.0;
        double r16763433 = r16763431 / r16763432;
        double r16763434 = z;
        double r16763435 = r16763433 - r16763434;
        double r16763436 = r16763430 * r16763435;
        double r16763437 = r16763426 + r16763436;
        return r16763437;
}
↓
double f(double x, double y, double z) {
        double r16763438 = x;
        double r16763439 = y;
        double r16763440 = r16763439 - r16763438;
        double r16763441 = 2.0;
        double r16763442 = 3.0;
        double r16763443 = r16763441 / r16763442;
        double r16763444 = z;
        double r16763445 = r16763443 - r16763444;
        double r16763446 = 6.0;
        double r16763447 = r16763445 * r16763446;
        double r16763448 = r16763440 * r16763447;
        double r16763449 = r16763438 + r16763448;
        return r16763449;
}

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

    \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6.0 \cdot \left(\frac{2.0}{3.0} - z\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))