Average Error: 0.1 → 0.1
Time: 11.4s
Precision: 64
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
↓
\[3 \cdot \left(y \cdot y\right) + x \cdot x\]
\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y
↓
3 \cdot \left(y \cdot y\right) + x \cdot x
double f(double x, double y) {
        double r22927050 = x;
        double r22927051 = r22927050 * r22927050;
        double r22927052 = y;
        double r22927053 = r22927052 * r22927052;
        double r22927054 = r22927051 + r22927053;
        double r22927055 = r22927054 + r22927053;
        double r22927056 = r22927055 + r22927053;
        return r22927056;
}
↓
double f(double x, double y) {
        double r22927057 = 3.0;
        double r22927058 = y;
        double r22927059 = r22927058 * r22927058;
        double r22927060 = r22927057 * r22927059;
        double r22927061 = x;
        double r22927062 = r22927061 * r22927061;
        double r22927063 = r22927060 + r22927062;
        return r22927063;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\left(y \cdot y\right) \cdot 3 + x \cdot x}\]

  3. Final simplification0.1

    \[\leadsto 3 \cdot \left(y \cdot y\right) + x \cdot x\]

Reproduce

herbie shell --seed 2019174 
(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)))