Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[\left(x + y\right) \cdot \left(x + y\right)\]
↓
\[\left({x}^{2} + {y}^{2}\right) + 2 \cdot \left(x \cdot y\right)\]
\left(x + y\right) \cdot \left(x + y\right)
↓
\left({x}^{2} + {y}^{2}\right) + 2 \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r666114 = x;
        double r666115 = y;
        double r666116 = r666114 + r666115;
        double r666117 = r666116 * r666116;
        return r666117;
}
↓
double f(double x, double y) {
        double r666118 = x;
        double r666119 = 2.0;
        double r666120 = pow(r666118, r666119);
        double r666121 = y;
        double r666122 = pow(r666121, r666119);
        double r666123 = r666120 + r666122;
        double r666124 = r666118 * r666121;
        double r666125 = r666119 * r666124;
        double r666126 = r666123 + r666125;
        return r666126;
}

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. Taylor expanded around 0 0.0

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

  8. Applied associate-+r+0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019353 
(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)))