Average Error: 0.4 → 0.4
Time: 27.8s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
\left(x + \left(\left(y - x\right) \cdot 6\right) \cdot \frac{2}{3}\right) + \left(-z\right) \cdot \left(\left(y - x\right) \cdot 6\right)
double f(double x, double y, double z) {
        double r200410 = x;
        double r200411 = y;
        double r200412 = r200411 - r200410;
        double r200413 = 6.0;
        double r200414 = r200412 * r200413;
        double r200415 = 2.0;
        double r200416 = 3.0;
        double r200417 = r200415 / r200416;
        double r200418 = z;
        double r200419 = r200417 - r200418;
        double r200420 = r200414 * r200419;
        double r200421 = r200410 + r200420;
        return r200421;
}
↓
double f(double x, double y, double z) {
        double r200422 = x;
        double r200423 = y;
        double r200424 = r200423 - r200422;
        double r200425 = 6.0;
        double r200426 = r200424 * r200425;
        double r200427 = 2.0;
        double r200428 = 3.0;
        double r200429 = r200427 / r200428;
        double r200430 = r200426 * r200429;
        double r200431 = r200422 + r200430;
        double r200432 = z;
        double r200433 = -r200432;
        double r200434 = r200433 * r200426;
        double r200435 = r200431 + r200434;
        return r200435;
}

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-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. Simplified0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019306 
(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))))