Average Error: 0.4 → 0.2
Time: 3.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(\left(y - x\right) \cdot \left(\frac{2}{3} \cdot 6\right) + \left(y - x\right) \cdot \left(\left(-z\right) \cdot 6\right)\right)
double f(double x, double y, double z) {
        double r300450 = x;
        double r300451 = y;
        double r300452 = r300451 - r300450;
        double r300453 = 6.0;
        double r300454 = r300452 * r300453;
        double r300455 = 2.0;
        double r300456 = 3.0;
        double r300457 = r300455 / r300456;
        double r300458 = z;
        double r300459 = r300457 - r300458;
        double r300460 = r300454 * r300459;
        double r300461 = r300450 + r300460;
        return r300461;
}
↓
double f(double x, double y, double z) {
        double r300462 = x;
        double r300463 = y;
        double r300464 = r300463 - r300462;
        double r300465 = 2.0;
        double r300466 = 3.0;
        double r300467 = r300465 / r300466;
        double r300468 = 6.0;
        double r300469 = r300467 * r300468;
        double r300470 = r300464 * r300469;
        double r300471 = z;
        double r300472 = -r300471;
        double r300473 = r300472 * r300468;
        double r300474 = r300464 * r300473;
        double r300475 = r300470 + r300474;
        double r300476 = r300462 + r300475;
        return r300476;
}

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. Using strategy rm

  5. Applied sub-neg0.2

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

  6. Applied distribute-lft-in0.2

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

  7. Applied distribute-lft-in0.2

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

  8. Simplified0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020039 
(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))))