Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
↓
\[x \cdot x + y \cdot \left(x \cdot 2 + y\right)\]
\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y
↓
x \cdot x + y \cdot \left(x \cdot 2 + y\right)
double f(double x, double y) {
        double r936126 = x;
        double r936127 = r936126 * r936126;
        double r936128 = 2.0;
        double r936129 = r936126 * r936128;
        double r936130 = y;
        double r936131 = r936129 * r936130;
        double r936132 = r936127 + r936131;
        double r936133 = r936130 * r936130;
        double r936134 = r936132 + r936133;
        return r936134;
}
↓
double f(double x, double y) {
        double r936135 = x;
        double r936136 = r936135 * r936135;
        double r936137 = y;
        double r936138 = 2.0;
        double r936139 = r936135 * r936138;
        double r936140 = r936139 + r936137;
        double r936141 = r936137 * r936140;
        double r936142 = r936136 + r936141;
        return r936142;
}

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
\[x \cdot x + \left(y \cdot y + \left(x \cdot y\right) \cdot 2\right)\]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + \left(x \cdot 2\right) \cdot y\right) + y \cdot y\]
  2. Using strategy rm

  3. Applied associate-+l+0.0

    \[\leadsto \color{blue}{x \cdot x + \left(\left(x \cdot 2\right) \cdot y + y \cdot y\right)}\]

  4. Simplified0.0

    \[\leadsto x \cdot x + \color{blue}{y \cdot \left(x \cdot 2 + y\right)}\]

  5. Final simplification0.0

    \[\leadsto x \cdot x + y \cdot \left(x \cdot 2 + y\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x y)
  :name "Examples.Basics.ProofTests:f4 from sbv-4.4"
  :precision binary64

  :herbie-target
  (+ (* x x) (+ (* y y) (* (* x y) 2)))

  (+ (+ (* x x) (* (* x 2) y)) (* y y)))