Average Error: 0.4 → 0.2
Time: 22.4s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(y - x\right) + x\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(6 \cdot \left(\frac{2}{3} - z\right)\right) \cdot \left(y - x\right) + x
double f(double x, double y, double z) {
        double r149424 = x;
        double r149425 = y;
        double r149426 = r149425 - r149424;
        double r149427 = 6.0;
        double r149428 = r149426 * r149427;
        double r149429 = 2.0;
        double r149430 = 3.0;
        double r149431 = r149429 / r149430;
        double r149432 = z;
        double r149433 = r149431 - r149432;
        double r149434 = r149428 * r149433;
        double r149435 = r149424 + r149434;
        return r149435;
}
↓
double f(double x, double y, double z) {
        double r149436 = 6.0;
        double r149437 = 2.0;
        double r149438 = 3.0;
        double r149439 = r149437 / r149438;
        double r149440 = z;
        double r149441 = r149439 - r149440;
        double r149442 = r149436 * r149441;
        double r149443 = y;
        double r149444 = x;
        double r149445 = r149443 - r149444;
        double r149446 = r149442 * r149445;
        double r149447 = r149446 + r149444;
        return r149447;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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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. Simplified0.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt11.9

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

  5. Applied associate-*r*12.4

    \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot \sqrt{\frac{2}{3} - z}\right) \cdot \sqrt{\frac{2}{3} - z}}, x\right)\]
  6. Using strategy rm

  7. Applied fma-udef12.5

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

  8. Simplified0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019347 +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))))