Average Error: 0.0 → 0.0
Time: 7.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left(x \cdot y + x \cdot y\right) + \left(x \cdot x + y \cdot y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left(x \cdot y + x \cdot y\right) + \left(x \cdot x + y \cdot y\right)
double f(double x, double y) {
        double r27895837 = x;
        double r27895838 = y;
        double r27895839 = r27895837 + r27895838;
        double r27895840 = r27895839 * r27895839;
        return r27895840;
}
↓
double f(double x, double y) {
        double r27895841 = x;
        double r27895842 = y;
        double r27895843 = r27895841 * r27895842;
        double r27895844 = r27895843 + r27895843;
        double r27895845 = r27895841 * r27895841;
        double r27895846 = r27895842 * r27895842;
        double r27895847 = r27895845 + r27895846;
        double r27895848 = r27895844 + r27895847;
        return r27895848;
}

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

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"

  :herbie-target
  (+ (* x x) (+ (* y y) (* 2.0 (* y x))))

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