Average Error: 0.1 → 0.1
Time: 9.5s
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 r429160 = x;
        double r429161 = r429160 * r429160;
        double r429162 = y;
        double r429163 = r429162 * r429162;
        double r429164 = r429161 + r429163;
        double r429165 = r429164 + r429163;
        double r429166 = r429165 + r429163;
        return r429166;
}
↓
double f(double x, double y) {
        double r429167 = x;
        double r429168 = r429167 * r429167;
        double r429169 = 3.0;
        double r429170 = y;
        double r429171 = r429169 * r429170;
        double r429172 = r429171 * r429170;
        double r429173 = r429168 + r429172;
        return r429173;
}

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 2019235 
(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)))