Average Error: 0.1 → 0.1
Time: 4.0s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[y \cdot y + \left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
y \cdot y + \left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right)
double f(double x, double y) {
        double r546978 = x;
        double r546979 = r546978 * r546978;
        double r546980 = y;
        double r546981 = r546980 * r546980;
        double r546982 = r546979 + r546981;
        double r546983 = r546982 + r546981;
        double r546984 = r546983 + r546981;
        return r546984;
}
↓
double f(double x, double y) {
        double r546985 = y;
        double r546986 = r546985 * r546985;
        double r546987 = x;
        double r546988 = r546987 * r546987;
        double r546989 = r546988 + r546986;
        double r546990 = r546989 + r546986;
        double r546991 = r546986 + r546990;
        return r546991;
}

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. Using strategy rm

  3. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{1 \cdot \left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right)} + y \cdot y\]

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))