Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot y + x \cdot \left(x + y \cdot 2\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot y + x \cdot \left(x + y \cdot 2\right)
double f(double x, double y) {
        double r532958 = x;
        double r532959 = y;
        double r532960 = r532958 + r532959;
        double r532961 = r532960 * r532960;
        return r532961;
}
↓
double f(double x, double y) {
        double r532962 = y;
        double r532963 = r532962 * r532962;
        double r532964 = x;
        double r532965 = 2.0;
        double r532966 = r532962 * r532965;
        double r532967 = r532964 + r532966;
        double r532968 = r532964 * r532967;
        double r532969 = r532963 + r532968;
        return r532969;
}

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

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

  3. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(y + 2 \cdot x\right) + x \cdot x}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"
  :precision binary64

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

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