Average Error: 38.6 → 0.0
Time: 22.7s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(x + 2\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(x + 2\right)
double f(double x) {
        double r723755 = x;
        double r723756 = 1.0;
        double r723757 = r723755 + r723756;
        double r723758 = r723757 * r723757;
        double r723759 = r723758 - r723756;
        return r723759;
}
↓
double f(double x) {
        double r723760 = x;
        double r723761 = 2.0;
        double r723762 = r723760 + r723761;
        double r723763 = r723760 * r723762;
        return r723763;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.6

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  5. Applied distribute-lft-out0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))