Average Error: 38.9 → 0.0
Time: 13.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[2 \cdot x + x \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
2 \cdot x + x \cdot x
double f(double x) {
        double r2927321 = x;
        double r2927322 = 1.0;
        double r2927323 = r2927321 + r2927322;
        double r2927324 = r2927323 * r2927323;
        double r2927325 = r2927324 - r2927322;
        return r2927325;
}
↓
double f(double x) {
        double r2927326 = 2.0;
        double r2927327 = x;
        double r2927328 = r2927326 * r2927327;
        double r2927329 = r2927327 * r2927327;
        double r2927330 = r2927328 + r2927329;
        return r2927330;
}

Error

Bits error versus x

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.9

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

  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. Final simplification0.0

    \[\leadsto 2 \cdot x + x \cdot x\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))