Average Error: 38.9 → 0.0
Time: 6.2s
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 r11293 = x;
        double r11294 = 1.0;
        double r11295 = r11293 + r11294;
        double r11296 = r11295 * r11295;
        double r11297 = r11296 - r11294;
        return r11297;
}
↓
double f(double x) {
        double r11298 = x;
        double r11299 = 2.0;
        double r11300 = r11299 + r11298;
        double r11301 = r11298 * r11300;
        return r11301;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.9

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))