Average Error: 38.5 → 0.0
Time: 18.6s
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 r690970 = x;
        double r690971 = 1.0;
        double r690972 = r690970 + r690971;
        double r690973 = r690972 * r690972;
        double r690974 = r690973 - r690971;
        return r690974;
}
↓
double f(double x) {
        double r690975 = x;
        double r690976 = 2.0;
        double r690977 = r690976 + r690975;
        double r690978 = r690975 * r690977;
        return r690978;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 38.5

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))