Average Error: 38.9 → 0.0
Time: 17.5s
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 r3069 = x;
        double r3070 = 1.0;
        double r3071 = r3069 + r3070;
        double r3072 = r3071 * r3071;
        double r3073 = r3072 - r3070;
        return r3073;
}
↓
double f(double x) {
        double r3074 = x;
        double r3075 = 2.0;
        double r3076 = r3074 + r3075;
        double r3077 = r3074 * r3076;
        return r3077;
}

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

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))