Average Error: 0.2 → 0.2
Time: 11.6s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(y - x\right) \cdot \left(z \cdot 6\right)\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(y - x\right) \cdot \left(z \cdot 6\right)
double f(double x, double y, double z) {
        double r598274 = x;
        double r598275 = y;
        double r598276 = r598275 - r598274;
        double r598277 = 6.0;
        double r598278 = r598276 * r598277;
        double r598279 = z;
        double r598280 = r598278 * r598279;
        double r598281 = r598274 + r598280;
        return r598281;
}
↓
double f(double x, double y, double z) {
        double r598282 = x;
        double r598283 = y;
        double r598284 = r598283 - r598282;
        double r598285 = z;
        double r598286 = 6.0;
        double r598287 = r598285 * r598286;
        double r598288 = r598284 * r598287;
        double r598289 = r598282 + r598288;
        return r598289;
}

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

Target

Original0.2
Target0.2
Herbie0.2
\[x - \left(6 \cdot z\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.2

    \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

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

  4. Simplified0.2

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

  5. Final simplification0.2

    \[\leadsto x + \left(y - x\right) \cdot \left(z \cdot 6\right)\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6 z) (- x y)))

  (+ x (* (* (- y x) 6) z)))