Average Error: 39.1 → 0.0
Time: 5.2s
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 r288856 = x;
        double r288857 = 1.0;
        double r288858 = r288856 + r288857;
        double r288859 = r288858 * r288858;
        double r288860 = r288859 - r288857;
        return r288860;
}
↓
double f(double x) {
        double r288861 = x;
        double r288862 = 2.0;
        double r288863 = r288861 + r288862;
        double r288864 = r288863 * r288861;
        return r288864;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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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 2019121 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))