Average Error: 0.1 → 0.1
Time: 41.8s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[y \cdot y + \left(\left(y \cdot y + x \cdot x\right) + y \cdot y\right)\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
y \cdot y + \left(\left(y \cdot y + x \cdot x\right) + y \cdot y\right)
double f(double x, double y) {
        double r27125107 = x;
        double r27125108 = r27125107 * r27125107;
        double r27125109 = y;
        double r27125110 = r27125109 * r27125109;
        double r27125111 = r27125108 + r27125110;
        double r27125112 = r27125111 + r27125110;
        double r27125113 = r27125112 + r27125110;
        return r27125113;
}
↓
double f(double x, double y) {
        double r27125114 = y;
        double r27125115 = r27125114 * r27125114;
        double r27125116 = x;
        double r27125117 = r27125116 * r27125116;
        double r27125118 = r27125115 + r27125117;
        double r27125119 = r27125118 + r27125115;
        double r27125120 = r27125115 + r27125119;
        return r27125120;
}

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

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

Reproduce

herbie shell --seed 2019200 
(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)))