Average Error: 38.2 → 0.0
Time: 11.7s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[{x}^{2} + 2 \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
{x}^{2} + 2 \cdot x
double f(double x) {
        double r3820 = x;
        double r3821 = 1.0;
        double r3822 = r3820 + r3821;
        double r3823 = r3822 * r3822;
        double r3824 = r3823 - r3821;
        return r3824;
}
↓
double f(double x) {
        double r3825 = x;
        double r3826 = 2.0;
        double r3827 = pow(r3825, r3826);
        double r3828 = 2.0;
        double r3829 = r3828 * r3825;
        double r3830 = r3827 + r3829;
        return r3830;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.2

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x + 2\right)}\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))