Incorect values for Jacobian when one of the outputs is built with intermediate steps

[ioanaif]

Code to reproduce:

int add(int a, int b) { return a + b ;}
void tes1(int a, int b, int* res){ 
    res[0] = a*10 + b*b*9;
    res[0] = add(res[0], 10);
    res[1] = a*a*9 + b*b*10;
}
void tes2(int a, int b, int* res){ 
    res[0] = a*10 + b*b*9;
    res[0] = res[0] + 10;
    res[1] = a*a*9 + b*b*10;
}
auto jacobian = clad::jacobian(test1);
int matr[4];
int res[2] = {0, 0};
jacobian.execute(3, 5, res, matr);

Both versions will output: [64, 190, 0, 0] as the Jacobian result gets summed column wise.

However, if the intermediate step is not present, then the corect result is computed: [10, 90, 54, 100]:

void tes3t(int a, int b, int* res){ 
    res[0] = a*10 + b*b*9 + 10;
    res[1] = a*a*9 + b*b*10;
}

In case of test1 and test2 the jacobianMatrix indexing is at fault:

--------------
{
        int _r6 = 1 * 9;
        int _r7 = _r6 * _t5;
        jacobianMatrix[0UL] += _r7;
        int _r8 = _t6 * _r6;
        jacobianMatrix[0UL] += _r8;
        int _r9 = 1 * 10;
        int _r10 = _r9 * _t7;
        jacobianMatrix[1UL] += _r10;
        int _r11 = _t8 * _r9;
        jacobianMatrix[1UL] += _r11;
    }
    {
        int _jac0 = 0;
        int _jac1 = 0;
        add_pullback(_t4, 10, 1, &_jac0, &_jac1);
        int _r4 = _jac0;
        int _r5 = _jac1;
    }
    {
        int _r0 = 1 * 10;
        jacobianMatrix[0UL] += _r0;
        int _r1 = 1 * 9;
        int _r2 = _r1 * _t2;
        jacobianMatrix[1UL] += _r2;
        int _r3 = _t3 * _r1;
        jacobianMatrix[1UL] += _r3;
    }
--------------

In the case of test3 the Jacobian is generated as:

--------------
{
        int _r4 = 1 * 9;
        int _r5 = _r4 * _t4;
        jacobianMatrix[2UL] += _r5;
        int _r6 = _t5 * _r4;
        jacobianMatrix[2UL] += _r6;
        int _r7 = 1 * 10;
        int _r8 = _r7 * _t6;
        jacobianMatrix[3UL] += _r8;
        int _r9 = _t7 * _r7;
        jacobianMatrix[3UL] += _r9;
    }
    {
        int _r0 = 1 * 10;
        jacobianMatrix[0UL] += _r0;
        int _r1 = 1 * 9;
        int _r2 = _r1 * _t2;
        jacobianMatrix[1UL] += _r2;
        int _r3 = _t3 * _r1;
        jacobianMatrix[1UL] += _r3;
    }
--------------

[davidlange6]

same problem as #473?