Average Error: 39.1 → 0.0
Time: 4.4s
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 r163870 = x;
        double r163871 = 1.0;
        double r163872 = r163870 + r163871;
        double r163873 = r163872 * r163872;
        double r163874 = r163873 - r163871;
        return r163874;
}
↓
double f(double x) {
        double r163875 = x;
        double r163876 = 2.0;
        double r163877 = r163876 + r163875;
        double r163878 = r163875 * r163877;
        return r163878;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.1

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019155 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))