Average Error: 0.0 → 0.0
Time: 4.2s
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 r767095 = x;
        double r767096 = r767095 * r767095;
        double r767097 = 2.0;
        double r767098 = r767095 * r767097;
        double r767099 = y;
        double r767100 = r767098 * r767099;
        double r767101 = r767096 + r767100;
        double r767102 = r767099 * r767099;
        double r767103 = r767101 + r767102;
        return r767103;
}
↓
double f(double x, double y) {
        double r767104 = y;
        double r767105 = x;
        double r767106 = 2.0;
        double r767107 = r767105 * r767106;
        double r767108 = r767107 + r767104;
        double r767109 = r767104 * r767108;
        double r767110 = r767105 * r767105;
        double r767111 = r767109 + r767110;
        return r767111;
}

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 2020060 
(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)))