Average Error: 38.9 → 0.0
Time: 24.0s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + 2 \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + 2 \cdot x
double f(double x) {
        double r950061 = x;
        double r950062 = 1.0;
        double r950063 = r950061 + r950062;
        double r950064 = r950063 * r950063;
        double r950065 = r950064 - r950062;
        return r950065;
}
↓
double f(double x) {
        double r950066 = x;
        double r950067 = r950066 * r950066;
        double r950068 = 2.0;
        double r950069 = r950068 * r950066;
        double r950070 = r950067 + r950069;
        return r950070;
}

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

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))