Average Error: 38.9 → 0.0
Time: 6.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + x \cdot 2\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + x \cdot 2
double f(double x) {
        double r591329 = x;
        double r591330 = 1.0;
        double r591331 = r591329 + r591330;
        double r591332 = r591331 * r591331;
        double r591333 = r591332 - r591330;
        return r591333;
}
↓
double f(double x) {
        double r591334 = x;
        double r591335 = r591334 * r591334;
        double r591336 = 2.0;
        double r591337 = r591334 * r591336;
        double r591338 = r591335 + r591337;
        return r591338;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 38.9

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

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x + 2\right)}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))