Average Error: 39.3 → 0.0
Time: 6.0s
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 r322830 = x;
        double r322831 = 1.0;
        double r322832 = r322830 + r322831;
        double r322833 = r322832 * r322832;
        double r322834 = r322833 - r322831;
        return r322834;
}
↓
double f(double x) {
        double r322835 = x;
        double r322836 = 2.0;
        double r322837 = r322835 + r322836;
        double r322838 = r322837 * r322835;
        return r322838;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019104 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))