Average Error: 0.2 → 0.2
Time: 20.3s
Precision: 64
\[x + \left(\left(y - x\right) \cdot 6\right) \cdot z\]
↓
\[x + \left(\left(y - x\right) \cdot z\right) \cdot 6\]
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
↓
x + \left(\left(y - x\right) \cdot z\right) \cdot 6
double f(double x, double y, double z) {
        double r655420 = x;
        double r655421 = y;
        double r655422 = r655421 - r655420;
        double r655423 = 6.0;
        double r655424 = r655422 * r655423;
        double r655425 = z;
        double r655426 = r655424 * r655425;
        double r655427 = r655420 + r655426;
        return r655427;
}
↓
double f(double x, double y, double z) {
        double r655428 = x;
        double r655429 = y;
        double r655430 = r655429 - r655428;
        double r655431 = z;
        double r655432 = r655430 * r655431;
        double r655433 = 6.0;
        double r655434 = r655432 * r655433;
        double r655435 = r655428 + r655434;
        return r655435;
}

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. Using strategy rm

  6. Applied associate-*r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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)))