Average Error: 0.1 → 0.1
Time: 14.2s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[y \cdot y + \left(y \cdot y + \left(x \cdot x + y \cdot y\right)\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
y \cdot y + \left(y \cdot y + \left(x \cdot x + y \cdot y\right)\right)
double f(double x, double y) {
        double r22419282 = x;
        double r22419283 = r22419282 * r22419282;
        double r22419284 = y;
        double r22419285 = r22419284 * r22419284;
        double r22419286 = r22419283 + r22419285;
        double r22419287 = r22419286 + r22419285;
        double r22419288 = r22419287 + r22419285;
        return r22419288;
}
↓
double f(double x, double y) {
        double r22419289 = y;
        double r22419290 = r22419289 * r22419289;
        double r22419291 = x;
        double r22419292 = r22419291 * r22419291;
        double r22419293 = r22419292 + r22419290;
        double r22419294 = r22419290 + r22419293;
        double r22419295 = r22419290 + r22419294;
        return r22419295;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"

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

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