Average Error: 0.0 → 0.0
Time: 5.8s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left(x + y\right) \cdot x + \left(x + y\right) \cdot y\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left(x + y\right) \cdot x + \left(x + y\right) \cdot y
double f(double x, double y) {
        double r853987 = x;
        double r853988 = y;
        double r853989 = r853987 + r853988;
        double r853990 = r853989 * r853989;
        return r853990;
}
↓
double f(double x, double y) {
        double r853991 = x;
        double r853992 = y;
        double r853993 = r853991 + r853992;
        double r853994 = r853993 * r853991;
        double r853995 = r853993 * r853992;
        double r853996 = r853994 + r853995;
        return r853996;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +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)))