Average Error: 0.0 → 0.0
Time: 1.5s
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 r675773 = x;
        double r675774 = y;
        double r675775 = r675773 + r675774;
        double r675776 = r675775 * r675775;
        return r675776;
}
↓
double f(double x, double y) {
        double r675777 = x;
        double r675778 = y;
        double r675779 = r675777 + r675778;
        double r675780 = r675779 + r675778;
        double r675781 = r675777 * r675780;
        double r675782 = r675778 * r675778;
        double r675783 = r675781 + r675782;
        return r675783;
}

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 2019354 
(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)))