Average Error: 39.1 → 0.0
Time: 55.0s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]
double f(double x) {
        double r6575420 = x;
        double r6575421 = 1.0;
        double r6575422 = r6575420 + r6575421;
        double r6575423 = r6575422 * r6575422;
        double r6575424 = r6575423 - r6575421;
        return r6575424;
}
↓
double f(double x) {
        double r6575425 = x;
        double r6575426 = 2.0;
        double r6575427 = r6575425 + r6575426;
        double r6575428 = r6575427 * r6575425;
        return r6575428;
}


\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 39.1

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

  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 2019102 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))