Average Error: 0.1 → 0.1
Time: 11.1s
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 r411278 = x;
        double r411279 = r411278 * r411278;
        double r411280 = y;
        double r411281 = r411280 * r411280;
        double r411282 = r411279 + r411281;
        double r411283 = r411282 + r411281;
        double r411284 = r411283 + r411281;
        return r411284;
}
↓
double f(double x, double y) {
        double r411285 = y;
        double r411286 = r411285 * r411285;
        double r411287 = x;
        double r411288 = r411287 * r411287;
        double r411289 = r411288 + r411286;
        double r411290 = r411286 + r411289;
        double r411291 = r411286 + r411290;
        return r411291;
}

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 2019195 
(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)))