CVXPY
Minimize
  QuadForm(Hstack(x, [1. 2.]), [[1.00 0.00 0.00 0.00]
 [0.00 1.00 0.00 0.00]
 [0.00 0.00 1.00 0.00]
 [0.00 0.00 0.00 1.00]])
Subject To
Bounds
 x free
End
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AFTER COMPILATION
Minimize
 Obj: +1 x_0
Subject to
 c1: +1 soc_t_0 -1 x_0 = +1
 c2: +1 soc_t_1 +1 x_0 = +1
 c3: +1 soc_t_2 -2 x_1 = +0
 c4: +1 soc_t_3 -2 x_2 = +0
 c5: +1 soc_t_4 = +2
 c6: +1 soc_t_5 = +4
 c7: + [ +1 soc_t_1 * soc_t_1 +1 soc_t_2 * soc_t_2 +1 soc_t_3 * soc_t_3 +1 soc_t_4 * soc_t_4 +1 soc_t_5 * soc_t_5
  -1 soc_t_0 * soc_t_0 ] <= +0
Bounds
 x_0 free
 x_1 free
 x_2 free
 soc_t_1 free
 soc_t_2 free
 soc_t_3 free
 soc_t_4 free
 soc_t_5 free
End
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SCIP
Minimize
 Obj: +1 x3
Subject to
 c1: +1 x3 + [ -1 x_0 * x_0 -1 x_1 * x_1 ] >= +5
Bounds
 x_0 free
 x_1 free
 x3 free
End