Average Error: 38.4 → 0.0
Time: 20.6s
Precision: 64
\[\left(x + 1.0\right) \cdot \left(x + 1.0\right) - 1.0\]
↓
\[x \cdot \left(2.0 + x\right)\]
\left(x + 1.0\right) \cdot \left(x + 1.0\right) - 1.0
↓
x \cdot \left(2.0 + x\right)
double f(double x) {
        double r625694 = x;
        double r625695 = 1.0;
        double r625696 = r625694 + r625695;
        double r625697 = r625696 * r625696;
        double r625698 = r625697 - r625695;
        return r625698;
}
↓
double f(double x) {
        double r625699 = x;
        double r625700 = 2.0;
        double r625701 = r625700 + r625699;
        double r625702 = r625699 * r625701;
        return r625702;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.4

    \[\left(x + 1.0\right) \cdot \left(x + 1.0\right) - 1.0\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2.0 \cdot x + {x}^{2}}\]

  3. Simplified0.0

    \[\leadsto \color{blue}{2.0 \cdot x + x \cdot x}\]
  4. Using strategy rm

  5. Applied distribute-rgt-out0.0

    \[\leadsto \color{blue}{x \cdot \left(2.0 + x\right)}\]

  6. Final simplification0.0

    \[\leadsto x \cdot \left(2.0 + x\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))