Average Error: 39.0 → 0.0
Time: 16.9s
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 r485087 = x;
        double r485088 = 1.0;
        double r485089 = r485087 + r485088;
        double r485090 = r485089 * r485089;
        double r485091 = r485090 - r485088;
        return r485091;
}
↓
double f(double x) {
        double r485092 = x;
        double r485093 = 2.0;
        double r485094 = r485093 + r485092;
        double r485095 = r485092 * r485094;
        return r485095;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 39.0

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

  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 2019151 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))