Average Error: 38.8 → 0.0
Time: 21.7s
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 r8913 = x;
        double r8914 = 1.0;
        double r8915 = r8913 + r8914;
        double r8916 = r8915 * r8915;
        double r8917 = r8916 - r8914;
        return r8917;
}
↓
double f(double x) {
        double r8918 = x;
        double r8919 = 2.0;
        double r8920 = r8918 * r8919;
        double r8921 = r8918 * r8918;
        double r8922 = r8920 + r8921;
        return r8922;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

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

  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 2019351 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))