Average Error: 0.4 → 0.4
Time: 7.7s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r277466 = x;
        double r277467 = y;
        double r277468 = r277467 - r277466;
        double r277469 = 6.0;
        double r277470 = r277468 * r277469;
        double r277471 = 2.0;
        double r277472 = 3.0;
        double r277473 = r277471 / r277472;
        double r277474 = z;
        double r277475 = r277473 - r277474;
        double r277476 = r277470 * r277475;
        double r277477 = r277466 + r277476;
        return r277477;
}
↓
double f(double x, double y, double z) {
        double r277478 = x;
        double r277479 = 2.0;
        double r277480 = 3.0;
        double r277481 = r277479 / r277480;
        double r277482 = y;
        double r277483 = r277482 - r277478;
        double r277484 = 6.0;
        double r277485 = r277483 * r277484;
        double r277486 = r277481 * r277485;
        double r277487 = r277478 + r277486;
        double r277488 = z;
        double r277489 = -r277488;
        double r277490 = r277489 * r277485;
        double r277491 = r277487 + r277490;
        return r277491;
}

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 sub-neg0.4

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

  4. Applied distribute-rgt-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020083 
(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))))