Average Error: 39.3 → 0.0
Time: 8.1s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + 2 \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + 2 \cdot x
double f(double x) {
        double r493960 = x;
        double r493961 = 1.0;
        double r493962 = r493960 + r493961;
        double r493963 = r493962 * r493962;
        double r493964 = r493963 - r493961;
        return r493964;
}
↓
double f(double x) {
        double r493965 = x;
        double r493966 = r493965 * r493965;
        double r493967 = 2.0;
        double r493968 = r493967 * r493965;
        double r493969 = r493966 + r493968;
        return r493969;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.3

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

  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. Final simplification0.0

    \[\leadsto x \cdot x + 2 \cdot x\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))