Average Error: 39.1 → 0.0
Time: 2.1s
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 r30773 = x;
        double r30774 = 1.0;
        double r30775 = r30773 + r30774;
        double r30776 = r30775 * r30775;
        double r30777 = r30776 - r30774;
        return r30777;
}
↓
double f(double x) {
        double r30778 = x;
        double r30779 = 2.0;
        double r30780 = r30778 + r30779;
        double r30781 = r30780 * r30778;
        return r30781;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))