Average Error: 0.4 → 0.2
Time: 5.4s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r258463 = x;
        double r258464 = y;
        double r258465 = r258464 - r258463;
        double r258466 = 6.0;
        double r258467 = r258465 * r258466;
        double r258468 = 2.0;
        double r258469 = 3.0;
        double r258470 = r258468 / r258469;
        double r258471 = z;
        double r258472 = r258470 - r258471;
        double r258473 = r258467 * r258472;
        double r258474 = r258463 + r258473;
        return r258474;
}
↓
double f(double x, double y, double z) {
        double r258475 = x;
        double r258476 = y;
        double r258477 = r258476 - r258475;
        double r258478 = 6.0;
        double r258479 = 2.0;
        double r258480 = 3.0;
        double r258481 = r258479 / r258480;
        double r258482 = z;
        double r258483 = r258481 - r258482;
        double r258484 = r258478 * r258483;
        double r258485 = r258477 * r258484;
        double r258486 = r258475 + r258485;
        return r258486;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 
(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))))