Average Error: 0.4 → 0.2
Time: 17.5s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2}{3} - z\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r275467 = x;
        double r275468 = y;
        double r275469 = r275468 - r275467;
        double r275470 = 6.0;
        double r275471 = r275469 * r275470;
        double r275472 = 2.0;
        double r275473 = 3.0;
        double r275474 = r275472 / r275473;
        double r275475 = z;
        double r275476 = r275474 - r275475;
        double r275477 = r275471 * r275476;
        double r275478 = r275467 + r275477;
        return r275478;
}
↓
double f(double x, double y, double z) {
        double r275479 = x;
        double r275480 = y;
        double r275481 = r275480 - r275479;
        double r275482 = 2.0;
        double r275483 = 3.0;
        double r275484 = r275482 / r275483;
        double r275485 = z;
        double r275486 = r275484 - r275485;
        double r275487 = 6.0;
        double r275488 = r275486 * r275487;
        double r275489 = r275481 * r275488;
        double r275490 = r275479 + r275489;
        return r275490;
}

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. Simplified0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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))))