Average Error: 39.3 → 0.0
Time: 9.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
\left(x + 2\right) \cdot x
double f(double x) {
        double r560860 = x;
        double r560861 = 1.0;
        double r560862 = r560860 + r560861;
        double r560863 = r560862 * r560862;
        double r560864 = r560863 - r560861;
        return r560864;
}
↓
double f(double x) {
        double r560865 = x;
        double r560866 = 2.0;
        double r560867 = r560865 + r560866;
        double r560868 = r560867 * r560865;
        return r560868;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.3

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

  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 2019130 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))