Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[y \cdot \left(x \cdot 2 + y\right) + x \cdot x\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
y \cdot \left(x \cdot 2 + y\right) + x \cdot x
double f(double x, double y) {
        double r689948 = x;
        double r689949 = r689948 * r689948;
        double r689950 = 2.0;
        double r689951 = r689948 * r689950;
        double r689952 = y;
        double r689953 = r689951 * r689952;
        double r689954 = r689949 + r689953;
        double r689955 = r689952 * r689952;
        double r689956 = r689954 + r689955;
        return r689956;
}
↓
double f(double x, double y) {
        double r689957 = y;
        double r689958 = x;
        double r689959 = 2.0;
        double r689960 = r689958 * r689959;
        double r689961 = r689960 + r689957;
        double r689962 = r689957 * r689961;
        double r689963 = r689958 * r689958;
        double r689964 = r689962 + r689963;
        return r689964;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot x + \left(y \cdot y + \left(x \cdot y\right) \cdot 2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]

  2. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(x \cdot 2 + y\right) + x \cdot x}\]

  3. Final simplification0.0

    \[\leadsto y \cdot \left(x \cdot 2 + y\right) + x \cdot x\]

Reproduce

herbie shell --seed 2020049 
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2)))

  (+ (+ (* x x) (* (* x 2) y)) (* y y)))