Average Error: 0.1 → 0.1
Time: 12.4s
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 r406507 = x;
        double r406508 = r406507 * r406507;
        double r406509 = y;
        double r406510 = r406509 * r406509;
        double r406511 = r406508 + r406510;
        double r406512 = r406511 + r406510;
        double r406513 = r406512 + r406510;
        return r406513;
}
↓
double f(double x, double y) {
        double r406514 = y;
        double r406515 = r406514 * r406514;
        double r406516 = x;
        double r406517 = r406516 * r406516;
        double r406518 = r406517 + r406515;
        double r406519 = r406515 + r406518;
        double r406520 = r406515 + r406519;
        return r406520;
}

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 2019194 
(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)))