Average Error: 38.9 → 0.0
Time: 8.8s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(2 + x\right)
double f(double x) {
        double r755960 = x;
        double r755961 = 1.0;
        double r755962 = r755960 + r755961;
        double r755963 = r755962 * r755962;
        double r755964 = r755963 - r755961;
        return r755964;
}
↓
double f(double x) {
        double r755965 = x;
        double r755966 = 2.0;
        double r755967 = r755966 + r755965;
        double r755968 = r755965 * r755967;
        return r755968;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.9

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Taylor expanded around 0 0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))