Average Error: 39.1 → 0.0
Time: 7.5s
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 r493881 = x;
        double r493882 = 1.0;
        double r493883 = r493881 + r493882;
        double r493884 = r493883 * r493883;
        double r493885 = r493884 - r493882;
        return r493885;
}
↓
double f(double x) {
        double r493886 = x;
        double r493887 = 2.0;
        double r493888 = r493887 + r493886;
        double r493889 = r493886 * r493888;
        return r493889;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot x + {x}^{2}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{2 \cdot x + x \cdot x}\]

  4. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot x + {x}^{2}}\]

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))