Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot x + y \cdot \left(\left(x + x\right) + y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot x + y \cdot \left(\left(x + x\right) + y\right)
double f(double x, double y) {
        double r481638 = x;
        double r481639 = y;
        double r481640 = r481638 + r481639;
        double r481641 = r481640 * r481640;
        return r481641;
}
↓
double f(double x, double y) {
        double r481642 = x;
        double r481643 = r481642 * r481642;
        double r481644 = y;
        double r481645 = r481642 + r481642;
        double r481646 = r481645 + r481644;
        double r481647 = r481644 * r481646;
        double r481648 = r481643 + r481647;
        return r481648;
}

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. Simplified0.0

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

  7. Applied distribute-lft-in0.0

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

  8. Applied associate-+l+0.0

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

  9. Simplified0.0

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

  11. Applied associate-+r+0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020003 
(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)))