Average Error: 0.1 → 0.1
Time: 7.1s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + \left(3 \cdot y\right) \cdot y\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
x \cdot x + \left(3 \cdot y\right) \cdot y
double f(double x, double y) {
        double r378329 = x;
        double r378330 = r378329 * r378329;
        double r378331 = y;
        double r378332 = r378331 * r378331;
        double r378333 = r378330 + r378332;
        double r378334 = r378333 + r378332;
        double r378335 = r378334 + r378332;
        return r378335;
}
↓
double f(double x, double y) {
        double r378336 = x;
        double r378337 = r378336 * r378336;
        double r378338 = 3.0;
        double r378339 = y;
        double r378340 = r378338 * r378339;
        double r378341 = r378340 * r378339;
        double r378342 = r378337 + r378341;
        return r378342;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot x + y \cdot \left(y + \left(y + y\right)\right)\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x \cdot x + 3 \cdot \left(y \cdot y\right)}\]
  3. Using strategy rm

  4. Applied associate-*r*0.1

    \[\leadsto x \cdot x + \color{blue}{\left(3 \cdot y\right) \cdot y}\]

  5. Final simplification0.1

    \[\leadsto x \cdot x + \left(3 \cdot y\right) \cdot y\]

Reproduce

herbie shell --seed 2019208 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"
  :precision binary64

  :herbie-target
  (+ (* x x) (* y (+ y (+ y y))))

  (+ (+ (+ (* x x) (* y y)) (* y y)) (* y y)))