Average Error: 38.4 → 0.0
Time: 25.7s
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 r13248 = x;
        double r13249 = 1.0;
        double r13250 = r13248 + r13249;
        double r13251 = r13250 * r13250;
        double r13252 = r13251 - r13249;
        return r13252;
}
↓
double f(double x) {
        double r13253 = x;
        double r13254 = r13253 * r13253;
        double r13255 = 2.0;
        double r13256 = r13255 * r13253;
        double r13257 = r13254 + r13256;
        return r13257;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.4

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

  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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))