Average Error: 0.4 → 0.4
Time: 3.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \frac{2}{3} \cdot \left(\left(y - x\right) \cdot 6\right)\right) + \left(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)\]
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(\left(y - x\right) \cdot 6\right) \cdot \left(-z\right)
double f(double x, double y, double z) {
        double r244371 = x;
        double r244372 = y;
        double r244373 = r244372 - r244371;
        double r244374 = 6.0;
        double r244375 = r244373 * r244374;
        double r244376 = 2.0;
        double r244377 = 3.0;
        double r244378 = r244376 / r244377;
        double r244379 = z;
        double r244380 = r244378 - r244379;
        double r244381 = r244375 * r244380;
        double r244382 = r244371 + r244381;
        return r244382;
}
↓
double f(double x, double y, double z) {
        double r244383 = x;
        double r244384 = 2.0;
        double r244385 = 3.0;
        double r244386 = r244384 / r244385;
        double r244387 = y;
        double r244388 = r244387 - r244383;
        double r244389 = 6.0;
        double r244390 = r244388 * r244389;
        double r244391 = r244386 * r244390;
        double r244392 = r244383 + r244391;
        double r244393 = z;
        double r244394 = -r244393;
        double r244395 = r244390 * r244394;
        double r244396 = r244392 + r244395;
        return r244396;
}

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. 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-lft-in0.4

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

  5. Applied associate-+r+0.4

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

  6. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019354 
(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))))