Average Error: 0.0 → 0.0
Time: 16.0s
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 r31318765 = x;
        double r31318766 = y;
        double r31318767 = r31318765 + r31318766;
        double r31318768 = r31318767 * r31318767;
        return r31318768;
}
↓
double f(double x, double y) {
        double r31318769 = x;
        double r31318770 = y;
        double r31318771 = r31318769 * r31318770;
        double r31318772 = r31318771 + r31318771;
        double r31318773 = r31318769 * r31318769;
        double r31318774 = r31318770 * r31318770;
        double r31318775 = r31318773 + r31318774;
        double r31318776 = r31318772 + r31318775;
        return r31318776;
}

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

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

  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 2019168 
(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)))