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unique_templates.json
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{
"templates": [
{
"equations": [
{
"symbols": [
"n_3",
"u_1_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "n_1*u_1_0 + n_2*u_0_0 - 1.0*n_3"
},
{
"symbols": [
"n_0",
"u_0_1",
"u_1_1"
],
"full": "-1.0*n_0 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "(-1.0*n_0*n_2 + 1.0*n_3)/(n_1 - n_2)"
},
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_0*n_1 - n_3)/(n_1 - n_2)"
}
}
},
{
"equations": [
{
"symbols": [
"u_1_0",
"u_0_0",
"n_1"
],
"full": "n_1 - 1.0*u_0_0 + u_1_0"
},
{
"symbols": [
"n_0",
"u_0_1",
"u_1_1"
],
"full": "-1.0*n_0 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_1"
],
"full": "0.5*n_0 - 0.5*n_1"
},
"u_0": {
"symbols": [
"n_0",
"n_1"
],
"full": "0.5*n_0 + 0.5*n_1"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "-1.0*n_0*u_0_0 - 1.0*n_1 + n_2*u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "-1.0*n_1/(n_0 - n_2)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_3",
"u_1_0",
"n_4"
],
"full": "-0.01*n_0*n_3 + 0.01*n_2*u_0_0 + 0.01*n_4*u_1_0"
},
{
"symbols": [
"u_0_1",
"u_1_1",
"n_1"
],
"full": "-1.0*n_1 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1",
"n_3",
"n_4"
],
"full": "(-1.0*n_0*n_3 + 1.0*n_1*n_2)/(n_2 - n_4)"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1",
"n_3",
"n_4"
],
"full": "1.0*(n_0*n_3 - n_1*n_4)/(n_2 - n_4)"
}
}
},
{
"equations": [
{
"symbols": [
"n_3",
"n_0",
"u_1_0",
"u_0_0",
"n_1"
],
"full": "n_0*u_1_0 + n_1*u_0_0 - 1.0*n_3"
},
{
"symbols": [
"u_0_1",
"n_2",
"u_1_1"
],
"full": "-1.0*n_2*u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "n_2*n_3/(1.0*n_0*n_2 + n_1)"
},
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*n_3/(n_0*n_2 + n_1)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"n_5",
"u_0_0",
"n_1"
],
"full": "-1.0*n_0 + n_1*u_1_0 + n_5*u_0_0"
},
{
"symbols": [
"n_3",
"u_0_1",
"n_2",
"u_1_1",
"n_4"
],
"full": "n_2*u_0_1 + n_3*u_1_1 - 1.0*n_4"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_3",
"n_5",
"n_1",
"n_4"
],
"full": "1.0*(n_0*n_2 - n_4*n_5)/(n_1*n_2 - n_3*n_5)"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_3",
"n_5",
"n_1",
"n_4"
],
"full": "1.0*(-n_0*n_3 + n_1*n_4)/(n_1*n_2 - n_3*n_5)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"n_2",
"u_0_0"
],
"full": "-1.0*n_0 + n_2*u_0_0 + n_2*u_1_0"
},
{
"symbols": [
"u_0_1",
"u_1_1",
"n_1"
],
"full": "-1.0*n_1 - 1.0*u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "0.5*n_0/n_2 + 0.5*n_1"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "0.5*n_0/n_2 - 0.5*n_1"
}
}
},
{
"equations": [
{
"symbols": [
"u_1_0",
"u_0_0",
"n_1"
],
"full": "-1.0*n_1 + u_0_0 + u_1_0"
},
{
"symbols": [
"n_0",
"u_0_1",
"n_2",
"u_1_1"
],
"full": "-1.0*n_0*u_1_1 - 1.0*n_2 + u_0_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_1 - n_2)/(n_0 + 1)"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_0*n_1 + n_2)/(n_0 + 1)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "-1.0*n_0 + n_1*u_0_0 - 1.0*n_2*u_1_0"
},
{
"symbols": [
"n_3",
"u_0_1",
"u_1_1"
],
"full": "-1.0*n_3 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "(-1.0*n_0 + 1.0*n_1*n_3)/(n_1 + n_2)"
},
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_0 + n_2*n_3)/(n_1 + n_2)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "n_0*u_0_0 - 1.0*n_1*u_0_0 - 1.0*n_2"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*n_2/(n_0 - n_1)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"n_1",
"n_3",
"u_0_0"
],
"full": "n_0 - 1.0*n_1 - 1.0*n_2*u_0_0 + n_3*u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_0 - n_1)/(n_2 - n_3)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"u_0_0"
],
"full": "-1.0*n_0 + 0.1*u_0_0 + 0.05*u_1_0"
},
{
"symbols": [
"u_0_1",
"u_1_1",
"n_1"
],
"full": "-1.0*n_1 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_1"
],
"full": "-20.0*n_0 + 2.0*n_1"
},
"u_0": {
"symbols": [
"n_0",
"n_1"
],
"full": "20.0*n_0 - 1.0*n_1"
}
}
},
{
"equations": [
{
"symbols": [
"n_3",
"u_1_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "0.01*n_1*u_1_0 - 1.0*n_2 + 0.01*n_3*u_0_0"
},
{
"symbols": [
"n_0",
"u_0_1",
"u_1_1"
],
"full": "-1.0*n_0 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "(-1.0*n_0*n_3 + 100.0*n_2)/(n_1 - n_3)"
},
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(1.0*n_0*n_1 - 100.0*n_2)/(n_1 - n_3)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "n_0 - 1.0*n_1 + 0.01*n_2*u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "100.0*(-n_0 + n_1)/n_2"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "n_0*u_1_0 - 1.0*n_1 + n_2*u_0_0"
},
{
"symbols": [
"n_3",
"u_0_1",
"u_1_1"
],
"full": "-1.0*n_3 - 1.0*u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_1 + n_2*n_3)/(n_0 + n_2)"
},
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(-n_0*n_3 + n_1)/(n_0 + n_2)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"u_0_0"
],
"full": "-1.0*n_0 + 2.0*u_0_0 + 4.0*u_1_0"
},
{
"symbols": [
"u_0_1",
"u_1_1",
"n_1"
],
"full": "-1.0*n_1 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_1"
],
"full": "0.5*n_0 - 1.0*n_1"
},
"u_0": {
"symbols": [
"n_0",
"n_1"
],
"full": "-0.5*n_0 + 2.0*n_1"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"n_2",
"u_0_0"
],
"full": "-1.0*n_0 + n_2*u_0_0 + n_2*u_1_0"
},
{
"symbols": [
"n_3",
"u_0_1",
"u_1_1",
"n_1"
],
"full": "-1.0*n_1 + n_3*u_0_1 - n_3*u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "0.5*n_0/n_2 - 0.5*n_1/n_3"
},
"u_0": {
"symbols": [
"n_3",
"n_0",
"n_2",
"n_1"
],
"full": "0.5*n_0/n_2 + 0.5*n_1/n_3"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_0_0",
"n_1"
],
"full": "n_0 - 1.0*n_1 + u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_1"
],
"full": "-n_0 + 1.0*n_1"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_1_0",
"u_0_0"
],
"full": "-1.0*n_0 + u_0_0 + u_1_0"
},
{
"symbols": [
"u_0_1",
"u_1_1",
"n_1"
],
"full": "-1.0*n_1*u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_1"
],
"full": "n_0*n_1/(1.0*n_1 + 1)"
},
"u_0": {
"symbols": [
"n_0",
"n_1"
],
"full": "1.0*n_0/(n_1 + 1)"
}
}
},
{
"equations": [
{
"symbols": [
"u_1_0",
"u_0_0",
"n_1"
],
"full": "-1.0*n_1 + u_0_0 + u_1_0"
},
{
"symbols": [
"n_0",
"u_0_1",
"n_2",
"u_1_1"
],
"full": "-1.0*n_0*u_1_1 + n_2 + u_0_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_1 + n_2)/(n_0 + 1)"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "(1.0*n_0*n_1 - n_2)/(1.0*n_0 + 1)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "-1.0*n_0 + n_1 + n_2*u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "(1.0*n_0 - n_1)/n_2"
}
}
},
{
"equations": [
{
"symbols": [
"u_1_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "-1.0*n_1*u_0_0 + n_2*u_1_0"
},
{
"symbols": [
"n_0",
"u_0_1",
"u_1_1"
],
"full": "-1.0*n_0 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*n_0*n_1/(n_1 + n_2)"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*n_0*n_2/(n_1 + n_2)"
}
}
},
{
"equations": [
{
"symbols": [
"n_3",
"n_0",
"u_1_0",
"u_0_0"
],
"full": "n_0*u_0_0 + n_0*u_1_0 - 1.0*n_3"
},
{
"symbols": [
"u_0_1",
"n_2",
"u_1_1",
"n_1",
"n_4"
],
"full": "-1.0*n_1*n_2*u_0_1 + n_2*u_1_1 - 1.0*n_4"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_3",
"n_1",
"n_4"
],
"full": "1.0*(n_0*n_4 + n_1*n_2*n_3)/(n_0*n_2*(n_1 + 1))"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1",
"n_3",
"n_4"
],
"full": "1.0*(-n_0*n_4 + n_2*n_3)/(n_0*n_2*(n_1 + 1))"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"u_0_0",
"n_1"
],
"full": "-1.0*n_0 + n_1*u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_1"
],
"full": "1.0*n_0/n_1"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "n_0*u_0_0 - 1.0*n_1 + n_2*u_0_0"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*n_1/(n_0 + n_2)"
}
}
},
{
"equations": [
{
"symbols": [
"n_2",
"u_0_0",
"n_1"
],
"full": "n_1*u_0_0 - 1.0*n_2"
},
{
"symbols": [
"n_0",
"u_1_0",
"u_0_1"
],
"full": "n_0*u_0_1 - 1.0*u_1_0"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*n_0*n_2/n_1"
},
"u_0": {
"symbols": [
"n_2",
"n_1"
],
"full": "1.0*n_2/n_1"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "-1.0*n_0 + n_1*u_0_0 - 1.0*n_2"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "1.0*(n_0 + n_2)/n_1"
}
}
},
{
"equations": [
{
"symbols": [
"u_1_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "-1.0*n_1 + n_2*u_0_0 - 1.0*u_1_0"
},
{
"symbols": [
"n_0",
"u_0_1",
"u_1_1"
],
"full": "n_0 + u_0_1 + u_1_1"
}
],
"solution": {
"u_1": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "-(1.0*n_0*n_2 + 1.0*n_1)/(n_2 + 1)"
},
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "(-n_0 + 1.0*n_1)/(1.0*n_2 + 1)"
}
}
},
{
"equations": [
{
"symbols": [
"n_0",
"n_2",
"u_0_0",
"n_1"
],
"full": "n_0 + n_1*u_0_0 + n_2"
}
],
"solution": {
"u_0": {
"symbols": [
"n_0",
"n_2",
"n_1"
],
"full": "-(n_0 + n_2)/n_1"
}
}
},
{
"equations": [
{
"symbols": [