Average Error: 0.0 → 0.0
Time: 9.4s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(y + x\right) + \left(x \cdot y + y \cdot y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(y + x\right) + \left(x \cdot y + y \cdot y\right)
double f(double x, double y) {
        double r531392 = x;
        double r531393 = y;
        double r531394 = r531392 + r531393;
        double r531395 = r531394 * r531394;
        return r531395;
}
↓
double f(double x, double y) {
        double r531396 = x;
        double r531397 = y;
        double r531398 = r531397 + r531396;
        double r531399 = r531396 * r531398;
        double r531400 = r531396 * r531397;
        double r531401 = r531397 * r531397;
        double r531402 = r531400 + r531401;
        double r531403 = r531399 + r531402;
        return r531403;
}

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

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

  7. Applied distribute-lft-in0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f3 from sbv-4.4"

  :herbie-target
  (+ (* x x) (+ (* y y) (* 2.0 (* y x))))

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