Average Error: 0.4 → 0.2
Time: 25.2s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]
x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)
↓
x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)
double f(double x, double y, double z) {
        double r13769318 = x;
        double r13769319 = y;
        double r13769320 = r13769319 - r13769318;
        double r13769321 = 6.0;
        double r13769322 = r13769320 * r13769321;
        double r13769323 = 2.0;
        double r13769324 = 3.0;
        double r13769325 = r13769323 / r13769324;
        double r13769326 = z;
        double r13769327 = r13769325 - r13769326;
        double r13769328 = r13769322 * r13769327;
        double r13769329 = r13769318 + r13769328;
        return r13769329;
}
↓
double f(double x, double y, double z) {
        double r13769330 = x;
        double r13769331 = y;
        double r13769332 = r13769331 - r13769330;
        double r13769333 = 2.0;
        double r13769334 = 3.0;
        double r13769335 = r13769333 / r13769334;
        double r13769336 = z;
        double r13769337 = r13769335 - r13769336;
        double r13769338 = 6.0;
        double r13769339 = r13769337 * r13769338;
        double r13769340 = r13769332 * r13769339;
        double r13769341 = r13769330 + r13769340;
        return r13769341;
}

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

    \[x + \left(\left(y - x\right) \cdot 6.0\right) \cdot \left(\frac{2.0}{3.0} - z\right)\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6.0 \cdot \left(\frac{2.0}{3.0} - z\right)\right)}\]

  4. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(\left(\frac{2.0}{3.0} - z\right) \cdot 6.0\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))