Average Error: 0.4 → 0.2
Time: 4.1s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)\]
↓
\[x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right)
↓
x + \left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)
double f(double x, double y, double z) {
        double r261203 = x;
        double r261204 = y;
        double r261205 = r261204 - r261203;
        double r261206 = 6.0;
        double r261207 = r261205 * r261206;
        double r261208 = 2.0;
        double r261209 = 3.0;
        double r261210 = r261208 / r261209;
        double r261211 = z;
        double r261212 = r261210 - r261211;
        double r261213 = r261207 * r261212;
        double r261214 = r261203 + r261213;
        return r261214;
}
↓
double f(double x, double y, double z) {
        double r261215 = x;
        double r261216 = y;
        double r261217 = r261216 - r261215;
        double r261218 = 6.0;
        double r261219 = 2.0;
        double r261220 = 3.0;
        double r261221 = r261219 / r261220;
        double r261222 = z;
        double r261223 = r261221 - r261222;
        double r261224 = r261218 * r261223;
        double r261225 = r261217 * r261224;
        double r261226 = r261215 + r261225;
        return r261226;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 
(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))))