Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot x + y \cdot \left(x + \left(x + y\right)\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot x + y \cdot \left(x + \left(x + y\right)\right)
double f(double x, double y) {
        double r639070 = x;
        double r639071 = y;
        double r639072 = r639070 + r639071;
        double r639073 = r639072 * r639072;
        return r639073;
}
↓
double f(double x, double y) {
        double r639074 = x;
        double r639075 = r639074 * r639074;
        double r639076 = y;
        double r639077 = r639074 + r639076;
        double r639078 = r639074 + r639077;
        double r639079 = r639076 * r639078;
        double r639080 = r639075 + r639079;
        return r639080;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  6. Applied distribute-lft-in0.0

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

  7. Applied associate-+l+0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))