Average Error: 38.8 → 0.0
Time: 5.7s
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 r16546 = x;
        double r16547 = 1.0;
        double r16548 = r16546 + r16547;
        double r16549 = r16548 * r16548;
        double r16550 = r16549 - r16547;
        return r16550;
}
↓
double f(double x) {
        double r16551 = x;
        double r16552 = 2.0;
        double r16553 = r16552 + r16551;
        double r16554 = r16551 * r16553;
        return r16554;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

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

  2. Simplified38.8

    \[\leadsto \color{blue}{\left(1 + x\right) \cdot \left(1 + x\right) - 1}\]

  3. Taylor expanded around 0 0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))