Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(\left(x + y\right) + y\right) + y \cdot y\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(\left(x + y\right) + y\right) + y \cdot y
double f(double x, double y) {
        double r675019 = x;
        double r675020 = y;
        double r675021 = r675019 + r675020;
        double r675022 = r675021 * r675021;
        return r675022;
}
↓
double f(double x, double y) {
        double r675023 = x;
        double r675024 = y;
        double r675025 = r675023 + r675024;
        double r675026 = r675025 + r675024;
        double r675027 = r675023 * r675026;
        double r675028 = r675024 * r675024;
        double r675029 = r675027 + r675028;
        return r675029;
}

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

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

  8. Applied associate-+r+0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(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)))