Average Error: 38.5 → 0.0
Time: 17.9s
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 r404213 = x;
        double r404214 = 1.0;
        double r404215 = r404213 + r404214;
        double r404216 = r404215 * r404215;
        double r404217 = r404216 - r404214;
        return r404217;
}
↓
double f(double x) {
        double r404218 = x;
        double r404219 = 2.0;
        double r404220 = r404218 + r404219;
        double r404221 = r404220 * r404218;
        return r404221;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.5

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

  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 2019139 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))