Average Error: 38.7 → 0.0
Time: 5.5s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]
double f(double x) {
        double r312551 = x;
        double r312552 = 1.0;
        double r312553 = r312551 + r312552;
        double r312554 = r312553 * r312553;
        double r312555 = r312554 - r312552;
        return r312555;
}
↓
double f(double x) {
        double r312556 = x;
        double r312557 = 2.0;
        double r312558 = r312556 + r312557;
        double r312559 = r312558 * r312556;
        return r312559;
}


\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 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))