Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[x \cdot \left(x + y\right) + y \cdot \left(x + y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
x \cdot \left(x + y\right) + y \cdot \left(x + y\right)
double f(double x, double y) {
        double r554100 = x;
        double r554101 = y;
        double r554102 = r554100 + r554101;
        double r554103 = r554102 * r554102;
        return r554103;
}
↓
double f(double x, double y) {
        double r554104 = x;
        double r554105 = y;
        double r554106 = r554104 + r554105;
        double r554107 = r554104 * r554106;
        double r554108 = r554105 * r554106;
        double r554109 = r554107 + r554108;
        return r554109;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +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)))