Average Error: 38.8 → 0.0
Time: 4.2s
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 r10924 = x;
        double r10925 = 1.0;
        double r10926 = r10924 + r10925;
        double r10927 = r10926 * r10926;
        double r10928 = r10927 - r10925;
        return r10928;
}
↓
double f(double x) {
        double r10929 = x;
        double r10930 = 2.0;
        double r10931 = r10930 + r10929;
        double r10932 = r10929 * r10931;
        return r10932;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

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

  2. Simplified38.8

    \[\leadsto \color{blue}{\left(1 + x\right) \cdot \left(1 + x\right) - 1}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))