user: What would the C source look like for the assembly code provided here?

```asm
<coeffs003>:
  endbr64
  mov    %rdx,%r8
  mov    %rcx,%rax
  movslq %esi,%rsi
  sub    %rsi,%rdi
  lea    0x10(,%rdi,8),%rdi
  lea    (%rdx,%rdi,1),%rcx
  movsd  (%rcx),%xmm8
  movapd %xmm0,%xmm6
  subsd  %xmm8,%xmm6
  lea    0x8(%rdx,%rdi,1),%rdx
  movsd  (%rdx),%xmm5
  movapd %xmm0,%xmm7
  subsd  %xmm5,%xmm7
  movapd %xmm6,%xmm3
  mulsd  %xmm7,%xmm3
  pxor   %xmm2,%xmm2
  addsd  %xmm2,%xmm3
  lea    -0x10(%r8,%rdi,1),%rsi
  movsd  (%rsi),%xmm12
  movapd %xmm0,%xmm1
  subsd  %xmm12,%xmm1
  movapd %xmm7,%xmm4
  mulsd  %xmm1,%xmm4
  addsd  %xmm4,%xmm3
  movapd %xmm6,%xmm11
  mulsd  %xmm1,%xmm11
  lea    -0x8(%r8,%rdi,1),%rdi
  movsd  (%rdi),%xmm9
  movapd %xmm9,%xmm10
  subsd  %xmm12,%xmm10
  movapd %xmm9,%xmm14
  subsd  %xmm8,%xmm14
  mulsd  %xmm10,%xmm14
  addsd  %xmm11,%xmm3
  movapd %xmm9,%xmm13
  subsd  %xmm5,%xmm13
  mulsd  %xmm14,%xmm13
  divsd  %xmm13,%xmm3
  mulsd  %xmm10,%xmm3
  addsd  %xmm2,%xmm3
  movapd %xmm0,%xmm13
  subsd  %xmm9,%xmm13
  mulsd  %xmm13,%xmm7
  addsd  %xmm2,%xmm7
  addsd  %xmm7,%xmm4
  mulsd  %xmm13,%xmm1
  movapd %xmm8,%xmm14
  subsd  %xmm12,%xmm14
  movapd %xmm8,%xmm7
  subsd  %xmm9,%xmm7
  mulsd  %xmm7,%xmm14
  addsd  %xmm1,%xmm4
  movapd %xmm8,%xmm7
  subsd  %xmm5,%xmm7
  mulsd  %xmm14,%xmm7
  divsd  %xmm7,%xmm4
  mulsd  %xmm10,%xmm4
  addsd  %xmm3,%xmm4
  mulsd  %xmm13,%xmm6
  addsd  %xmm2,%xmm6
  addsd  %xmm6,%xmm11
  movapd %xmm5,%xmm3
  subsd  %xmm12,%xmm3
  movapd %xmm5,%xmm6
  subsd  %xmm9,%xmm6
  mulsd  %xmm6,%xmm3
  addsd  %xmm11,%xmm1
  subsd  %xmm8,%xmm5
  mulsd  %xmm3,%xmm5
  divsd  %xmm5,%xmm1
  mulsd  %xmm10,%xmm1
  addsd  %xmm4,%xmm1
  movsd  %xmm1,(%rax)
  movsd  (%rdi),%xmm8
  movapd %xmm0,%xmm6
  subsd  %xmm8,%xmm6
  movsd  (%rdx),%xmm4
  movapd %xmm0,%xmm1
  subsd  %xmm4,%xmm1
  movapd %xmm6,%xmm3
  mulsd  %xmm1,%xmm3
  addsd  %xmm2,%xmm3
  movsd  (%rsi),%xmm9
  movapd %xmm0,%xmm5
  subsd  %xmm9,%xmm5
  mulsd  %xmm5,%xmm1
  addsd  %xmm3,%xmm1
  movapd %xmm6,%xmm3
  mulsd  %xmm5,%xmm3
  movsd  (%rcx),%xmm10
  movapd %xmm10,%xmm7
  subsd  %xmm8,%xmm7
  movapd %xmm10,%xmm12
  subsd  %xmm9,%xmm12
  mulsd  %xmm7,%xmm12
  addsd  %xmm3,%xmm1
  movapd %xmm10,%xmm11
  subsd  %xmm4,%xmm11
  mulsd  %xmm12,%xmm11
  divsd  %xmm11,%xmm1
  mulsd  %xmm7,%xmm1
  addsd  %xmm2,%xmm1
  movapd %xmm0,%xmm11
  subsd  %xmm10,%xmm11
  mulsd  %xmm11,%xmm6
  addsd  %xmm2,%xmm6
  mulsd  %xmm11,%xmm5
  addsd  %xmm6,%xmm5
  movapd %xmm4,%xmm6
  subsd  %xmm9,%xmm6
  movapd %xmm4,%xmm9
  subsd  %xmm8,%xmm9
  mulsd  %xmm9,%xmm6
  addsd  %xmm5,%xmm3
  subsd  %xmm10,%xmm4
  mulsd  %xmm6,%xmm4
  divsd  %xmm4,%xmm3
  mulsd  %xmm7,%xmm3
  addsd  %xmm1,%xmm3
  movsd  %xmm3,0x8(%rax)
  movsd  (%rdi),%xmm7
  movapd %xmm0,%xmm1
  subsd  %xmm7,%xmm1
  movsd  (%rcx),%xmm6
  movapd %xmm0,%xmm3
  subsd  %xmm6,%xmm3
  movapd %xmm1,%xmm4
  mulsd  %xmm3,%xmm4
  addsd  %xmm2,%xmm4
  movsd  (%rsi),%xmm8
  subsd  %xmm8,%xmm0
  mulsd  %xmm0,%xmm3
  addsd  %xmm3,%xmm4
  movsd  (%rdx),%xmm3
  movapd %xmm3,%xmm5
  subsd  %xmm8,%xmm5
  movapd %xmm3,%xmm8
  subsd  %xmm7,%xmm8
  mulsd  %xmm8,%xmm5
  subsd  %xmm6,%xmm3
  mulsd  %xmm0,%xmm1
  addsd  %xmm4,%xmm1
  movapd %xmm5,%xmm0
  mulsd  %xmm3,%xmm0
  divsd  %xmm0,%xmm1
  mulsd  %xmm3,%xmm1
  addsd  %xmm2,%xmm1
  movsd  %xmm1,0x10(%rax)
  ret
```

assistant: ```c
void coeffs003(double xi, long int i, int r, double *x, double *c) {
  double sum_l, sum_m, prod_n, prod_m;
  sum_l = 0.0;
  sum_m = 0.0;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 2];
  prod_n *= xi - x[i - r + 3];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 3];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_m = 1.0;
  prod_m *= x[i - r + 1] - x[i - r + 0];
  prod_m *= x[i - r + 1] - x[i - r + 2];
  prod_m *= x[i - r + 1] - x[i - r + 3];
  sum_l += sum_m / prod_m * (x[i - r + 0 + 1] - x[i - r + 0]);
  sum_m = 0.0;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 1];
  prod_n *= xi - x[i - r + 3];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 3];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 1];
  sum_m += prod_n;
  prod_m = 1.0;
  prod_m *= x[i - r + 2] - x[i - r + 0];
  prod_m *= x[i - r + 2] - x[i - r + 1];
  prod_m *= x[i - r + 2] - x[i - r + 3];
  sum_l += sum_m / prod_m * (x[i - r + 0 + 1] - x[i - r + 0]);
  sum_m = 0.0;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 1];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 1];
  sum_m += prod_n;
  prod_m = 1.0;
  prod_m *= x[i - r + 3] - x[i - r + 0];
  prod_m *= x[i - r + 3] - x[i - r + 1];
  prod_m *= x[i - r + 3] - x[i - r + 2];
  sum_l += sum_m / prod_m * (x[i - r + 0 + 1] - x[i - r + 0]);
  c[0] = sum_l;
  sum_l = 0.0;
  sum_m = 0.0;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 1];
  prod_n *= xi - x[i - r + 3];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 3];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 1];
  sum_m += prod_n;
  prod_m = 1.0;
  prod_m *= x[i - r + 2] - x[i - r + 0];
  prod_m *= x[i - r + 2] - x[i - r + 1];
  prod_m *= x[i - r + 2] - x[i - r + 3];
  sum_l += sum_m / prod_m * (x[i - r + 1 + 1] - x[i - r + 1]);
  sum_m = 0.0;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 1];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 1];
  sum_m += prod_n;
  prod_m = 1.0;
  prod_m *= x[i - r + 3] - x[i - r + 0];
  prod_m *= x[i - r + 3] - x[i - r + 1];
  prod_m *= x[i - r + 3] - x[i - r + 2];
  sum_l += sum_m / prod_m * (x[i - r + 1 + 1] - x[i - r + 1]);
  c[1] = sum_l;
  sum_l = 0.0;
  sum_m = 0.0;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 1];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 2];
  sum_m += prod_n;
  prod_n = 1.0;
  prod_n *= xi - x[i - r + 0];
  prod_n *= xi - x[i - r + 1];
  sum_m += prod_n;
  prod_m = 1.0;
  prod_m *= x[i - r + 3] - x[i - r + 0];
  prod_m *= x[i - r + 3] - x[i - r + 1];
  prod_m *= x[i - r + 3] - x[i - r + 2];
  sum_l += sum_m / prod_m * (x[i - r + 2 + 1] - x[i - r + 2]);
  c[2] = sum_l;
}
```