Average Error: 39.2 → 0.0
Time: 21.2s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot 2 + x \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot 2 + x \cdot x
double f(double x) {
        double r11362 = x;
        double r11363 = 1.0;
        double r11364 = r11362 + r11363;
        double r11365 = r11364 * r11364;
        double r11366 = r11365 - r11363;
        return r11366;
}
↓
double f(double x) {
        double r11367 = x;
        double r11368 = 2.0;
        double r11369 = r11367 * r11368;
        double r11370 = r11367 * r11367;
        double r11371 = r11369 + r11370;
        return r11371;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.2

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

  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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))