Average Error: 0.0 → 0.0
Time: 6.3s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[y \cdot y + \left(\left(2 \cdot x\right) \cdot y + x \cdot x\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
y \cdot y + \left(\left(2 \cdot x\right) \cdot y + x \cdot x\right)
double f(double x, double y) {
        double r434000 = x;
        double r434001 = y;
        double r434002 = r434000 + r434001;
        double r434003 = r434002 * r434002;
        return r434003;
}
↓
double f(double x, double y) {
        double r434004 = y;
        double r434005 = r434004 * r434004;
        double r434006 = 2.0;
        double r434007 = x;
        double r434008 = r434006 * r434007;
        double r434009 = r434008 * r434004;
        double r434010 = r434007 * r434007;
        double r434011 = r434009 + r434010;
        double r434012 = r434005 + r434011;
        return r434012;
}

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. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{y \cdot \left(y + 2 \cdot x\right) + x \cdot x}\]
  4. Using strategy rm

  5. Applied distribute-rgt-in0.0

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

  6. Applied associate-+l+0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 
(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)))