Average Error: 38.7 → 0.0
Time: 10.1s
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 r787984 = x;
        double r787985 = 1.0;
        double r787986 = r787984 + r787985;
        double r787987 = r787986 * r787986;
        double r787988 = r787987 - r787985;
        return r787988;
}
↓
double f(double x) {
        double r787989 = x;
        double r787990 = 2.0;
        double r787991 = r787989 + r787990;
        double r787992 = r787991 * r787989;
        return r787992;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 2019124 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))