Average Error: 39.5 → 0.0
Time: 4.3s
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 r163109 = x;
        double r163110 = 1.0;
        double r163111 = r163109 + r163110;
        double r163112 = r163111 * r163111;
        double r163113 = r163112 - r163110;
        return r163113;
}
↓
double f(double x) {
        double r163114 = x;
        double r163115 = r163114 * r163114;
        double r163116 = 2.0;
        double r163117 = r163114 * r163116;
        double r163118 = r163115 + r163117;
        return r163118;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.5

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

  2. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))