Average Error: 38.8 → 0.0
Time: 13.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(2 + x\right)
double f(double x) {
        double r343980 = x;
        double r343981 = 1.0;
        double r343982 = r343980 + r343981;
        double r343983 = r343982 * r343982;
        double r343984 = r343983 - r343981;
        return r343984;
}
↓
double f(double x) {
        double r343985 = x;
        double r343986 = 2.0;
        double r343987 = r343986 + r343985;
        double r343988 = r343985 * r343987;
        return r343988;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

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

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(2 + x\right)}\]

  3. Final simplification0.0

    \[\leadsto x \cdot \left(2 + x\right)\]

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))