Average Error: 38.7 → 0.0
Time: 5.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]
double f(double x) {
        double r288849 = x;
        double r288850 = 1.0;
        double r288851 = r288849 + r288850;
        double r288852 = r288851 * r288851;
        double r288853 = r288852 - r288850;
        return r288853;
}
↓
double f(double x) {
        double r288854 = x;
        double r288855 = 2.0;
        double r288856 = r288854 + r288855;
        double r288857 = r288856 * r288854;
        return r288857;
}


\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
\left(x + 2\right) \cdot x

Error

Bits error versus x

Derivation

  1. Initial program 38.7

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019101 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))