user: Translate the below assembly code into C programming language:

```asm
<gsw_rho_first_derivatives>:
  endbr64
  push   %r12
  push   %rbp
  push   %rbx
  sub    $0x20,%rsp
  movapd %xmm0,%xmm6
  movsd  %xmm0,0x10(%rsp)
  movsd  %xmm1,0x18(%rsp)
  movsd  %xmm2,0x8(%rsp)
  mov    %rdi,%r12
  mov    %rsi,%rbp
  mov    %rdx,%rbx
  pxor   %xmm0,%xmm0
  ucomisd %xmm6,%xmm0
  ja     L7
  sqrtsd %xmm6,%xmm6
  movapd %xmm6,%xmm9
L14:
  movsd  0x18(%rsp),%xmm15
  movapd %xmm15,%xmm7
  mulsd  D573(%rip),%xmm7
  subsd  D12(%rip),%xmm7
  movapd %xmm15,%xmm3
  mulsd  %xmm15,%xmm7
  subsd  D666(%rip),%xmm7
  movsd  D508(%rip),%xmm11
  mulsd  %xmm15,%xmm11
  subsd  D576(%rip),%xmm11
  movapd %xmm15,%xmm6
  mulsd  D957(%rip),%xmm6
  subsd  D717(%rip),%xmm6
  mulsd  %xmm15,%xmm6
  subsd  D676(%rip),%xmm6
  movsd  0x10(%rsp),%xmm8
  movapd %xmm8,%xmm0
  mulsd  %xmm11,%xmm0
  addsd  %xmm0,%xmm6
  movapd %xmm15,%xmm1
  mulsd  D855(%rip),%xmm1
  addsd  D721(%rip),%xmm1
  mulsd  %xmm15,%xmm1
  addsd  D870(%rip),%xmm1
  mulsd  %xmm15,%xmm1
  subsd  D464(%rip),%xmm1
  mulsd  %xmm15,%xmm1
  subsd  D237(%rip),%xmm1
  mulsd  D102(%rip),%xmm3
  addsd  D425(%rip),%xmm3
  mulsd  %xmm15,%xmm3
  subsd  D645(%rip),%xmm3
  mulsd  %xmm15,%xmm3
  subsd  D385(%rip),%xmm3
  movsd  D346(%rip),%xmm10
  movapd %xmm15,%xmm0
  mulsd  %xmm10,%xmm0
  subsd  D619(%rip),%xmm0
  movapd %xmm8,%xmm2
  mulsd  %xmm8,%xmm0
  addsd  %xmm0,%xmm3
  movsd  D19(%rip),%xmm5
  movapd %xmm8,%xmm12
  mulsd  %xmm5,%xmm12
  movapd %xmm15,%xmm14
  mulsd  D910(%rip),%xmm14
  movapd %xmm15,%xmm13
  mulsd  D634(%rip),%xmm13
  movapd %xmm15,%xmm0
  mulsd  D28(%rip),%xmm0
  subsd  D555(%rip),%xmm0
  mulsd  %xmm15,%xmm0
  subsd  D76(%rip),%xmm0
  mulsd  %xmm15,%xmm0
  addsd  D805(%rip),%xmm0
  mulsd  %xmm15,%xmm0
  subsd  D301(%rip),%xmm0
  mulsd  %xmm9,%xmm0
  mulsd  D800(%rip),%xmm2
  addsd  %xmm1,%xmm2
  addsd  %xmm2,%xmm0
  mulsd  %xmm8,%xmm0
  movapd %xmm15,%xmm2
  mulsd  D158(%rip),%xmm2
  addsd  D266(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  subsd  D857(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  addsd  D13(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  movsd  D60(%rip),%xmm8
  addsd  %xmm8,%xmm2
  addsd  %xmm2,%xmm0
  movapd %xmm15,%xmm2
  mulsd  D316(%rip),%xmm2
  subsd  D78(%rip),%xmm2
  addsd  %xmm12,%xmm2
  mulsd  %xmm15,%xmm2
  subsd  D431(%rip),%xmm2
  movsd  D494(%rip),%xmm4
  mulsd  %xmm15,%xmm4
  subsd  D501(%rip),%xmm4
  mulsd  0x8(%rsp),%xmm4
  addsd  %xmm4,%xmm2
  movsd  0x8(%rsp),%xmm4
  mulsd  %xmm4,%xmm2
  addsd  %xmm3,%xmm2
  mulsd  %xmm4,%xmm2
  addsd  %xmm0,%xmm2
  divsd  %xmm2,%xmm8
  movapd %xmm15,%xmm0
  mulsd  D701(%rip),%xmm0
  subsd  D733(%rip),%xmm0
  mulsd  %xmm15,%xmm0
  addsd  D246(%rip),%xmm0
  mulsd  %xmm15,%xmm0
  subsd  D232(%rip),%xmm0
  mulsd  %xmm9,%xmm0
  addsd  %xmm7,%xmm0
  mulsd  0x10(%rsp),%xmm0
  movapd %xmm15,%xmm2
  mulsd  D806(%rip),%xmm2
  subsd  D728(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  addsd  D650(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  addsd  D204(%rip),%xmm2
  addsd  %xmm2,%xmm0
  movapd %xmm15,%xmm2
  mulsd  D72(%rip),%xmm2
  subsd  D742(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  subsd  D954(%rip),%xmm2
  movsd  D61(%rip),%xmm4
  movsd  0x10(%rsp),%xmm15
  mulsd  %xmm4,%xmm15
  addsd  %xmm15,%xmm2
  movsd  0x8(%rsp),%xmm15
  mulsd  %xmm15,%xmm2
  addsd  %xmm6,%xmm2
  mulsd  %xmm15,%xmm2
  addsd  %xmm2,%xmm0
  mulsd  %xmm8,%xmm0
  movsd  0x18(%rsp),%xmm15
  movapd %xmm15,%xmm2
  mulsd  D352(%rip),%xmm2
  subsd  D882(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  addsd  D366(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  subsd  D190(%rip),%xmm2
  mulsd  %xmm9,%xmm2
  addsd  %xmm7,%xmm2
  movsd  0x8(%rsp),%xmm7
  mulsd  %xmm7,%xmm4
  addsd  %xmm11,%xmm4
  mulsd  %xmm7,%xmm4
  addsd  %xmm2,%xmm4
  movapd %xmm15,%xmm2
  mulsd  D740(%rip),%xmm2
  subsd  D162(%rip),%xmm2
  movapd %xmm15,%xmm7
  mulsd  %xmm15,%xmm2
  subsd  D445(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  addsd  D223(%rip),%xmm2
  mulsd  %xmm15,%xmm2
  subsd  D15(%rip),%xmm2
  mulsd  %xmm9,%xmm2
  addsd  %xmm2,%xmm1
  movsd  0x10(%rsp),%xmm11
  movapd %xmm11,%xmm2
  mulsd  D618(%rip),%xmm2
  addsd  %xmm2,%xmm1
  movsd  0x8(%rsp),%xmm15
  mulsd  %xmm15,%xmm5
  addsd  %xmm10,%xmm5
  mulsd  %xmm7,%xmm5
  subsd  D619(%rip),%xmm5
  mulsd  %xmm15,%xmm5
  addsd  %xmm5,%xmm1
  mulsd  %xmm0,%xmm1
  subsd  %xmm1,%xmm4
  mulsd  %xmm8,%xmm4
  movsd  %xmm4,(%r12)
  movapd %xmm7,%xmm1
  mulsd  D50(%rip),%xmm1
  subsd  D184(%rip),%xmm1
  mulsd  %xmm7,%xmm1
  addsd  D246(%rip),%xmm1
  mulsd  %xmm9,%xmm1
  movapd %xmm7,%xmm2
  mulsd  D912(%rip),%xmm2
  subsd  D12(%rip),%xmm2
  addsd  %xmm2,%xmm1
  mulsd  %xmm11,%xmm1
  movapd %xmm7,%xmm2
  mulsd  D405(%rip),%xmm2
  subsd  D336(%rip),%xmm2
  mulsd  %xmm7,%xmm2
  addsd  D650(%rip),%xmm2
  addsd  %xmm1,%xmm2
  movapd %xmm7,%xmm1
  mulsd  D217(%rip),%xmm1
  subsd  D717(%rip),%xmm1
  movsd  D508(%rip),%xmm4
  mulsd  %xmm11,%xmm4
  addsd  %xmm1,%xmm4
  movapd %xmm14,%xmm1
  subsd  D742(%rip),%xmm1
  mulsd  %xmm15,%xmm1
  addsd  %xmm1,%xmm4
  mulsd  %xmm15,%xmm4
  addsd  %xmm2,%xmm4
  movapd %xmm7,%xmm2
  mulsd  D716(%rip),%xmm2
  subsd  D363(%rip),%xmm2
  mulsd  %xmm7,%xmm2
  subsd  D517(%rip),%xmm2
  mulsd  %xmm7,%xmm2
  addsd  D805(%rip),%xmm2
  mulsd  %xmm9,%xmm2
  movapd %xmm7,%xmm1
  mulsd  D833(%rip),%xmm1
  addsd  D696(%rip),%xmm1
  mulsd  %xmm7,%xmm1
  addsd  D731(%rip),%xmm1
  mulsd  %xmm7,%xmm1
  subsd  D464(%rip),%xmm1
  addsd  %xmm1,%xmm2
  mulsd  %xmm11,%xmm2
  movapd %xmm7,%xmm1
  mulsd  D446(%rip),%xmm1
  addsd  D62(%rip),%xmm1
  mulsd  %xmm7,%xmm1
  subsd  D386(%rip),%xmm1
  mulsd  %xmm7,%xmm1
  addsd  D13(%rip),%xmm1
  addsd  %xmm2,%xmm1
  movapd %xmm7,%xmm2
  mulsd  D714(%rip),%xmm2
  addsd  D627(%rip),%xmm2
  mulsd  %xmm7,%xmm2
  subsd  D645(%rip),%xmm2
  mulsd  %xmm11,%xmm10
  addsd  %xmm2,%xmm10
  movapd %xmm13,%xmm2
  subsd  D78(%rip),%xmm2
  addsd  %xmm12,%xmm2
  movsd  D494(%rip),%xmm5
  mulsd  %xmm15,%xmm5
  addsd  %xmm5,%xmm2
  mulsd  %xmm15,%xmm2
  addsd  %xmm10,%xmm2
  mulsd  %xmm15,%xmm2
  addsd  %xmm2,%xmm1
  mulsd  %xmm0,%xmm1
  subsd  %xmm1,%xmm4
  mulsd  %xmm8,%xmm4
  movsd  %xmm4,0x0(%rbp)
  movapd %xmm14,%xmm1
  subsd  D118(%rip),%xmm1
  mulsd  %xmm7,%xmm1
  subsd  D793(%rip),%xmm1
  movapd %xmm11,%xmm2
  mulsd  D828(%rip),%xmm2
  addsd  %xmm2,%xmm1
  mulsd  %xmm15,%xmm1
  addsd  %xmm1,%xmm6
  movapd %xmm13,%xmm1
  subsd  D378(%rip),%xmm1
  mulsd  D591(%rip),%xmm11
  addsd  %xmm11,%xmm1
  mulsd  %xmm7,%xmm1
  movapd %xmm1,%xmm4
  subsd  D413(%rip),%xmm4
  mulsd  D609(%rip),%xmm7
  movapd %xmm7,%xmm1
  subsd  D177(%rip),%xmm1
  mulsd  %xmm15,%xmm1
  addsd  %xmm4,%xmm1
  mulsd  %xmm15,%xmm1
  addsd  %xmm3,%xmm1
  mulsd  %xmm0,%xmm1
  subsd  %xmm1,%xmm6
  movapd %xmm6,%xmm0
  mulsd  D661(%rip),%xmm0
  mulsd  %xmm8,%xmm0
  movsd  %xmm0,(%rbx)
  add    $0x20,%rsp
  pop    %rbx
  pop    %rbp
  pop    %r12
  ret
L7:
  movsd  0x10(%rsp),%xmm0
  call   <sqrt@plt>
  movapd %xmm0,%xmm9
  jmp    L14
```

tool_calls: name: parse_data
arguments: tag: D573
type_guessed: byte[8]
name: parse_data
arguments: tag: D12
type_guessed: byte[8]
name: parse_data
arguments: tag: D666
type_guessed: f64
name: parse_data
arguments: tag: D508
type_guessed: byte[8]
name: parse_data
arguments: tag: D576
type_guessed: byte[8]
name: parse_data
arguments: tag: D957
type_guessed: byte[8]
name: parse_data
arguments: tag: D717
type_guessed: byte[8]
name: parse_data
arguments: tag: D676
type_guessed: byte[8]
name: parse_data
arguments: tag: D855
type_guessed: byte[8]
name: parse_data
arguments: tag: D721
type_guessed: byte[8]
name: parse_data
arguments: tag: D870
type_guessed: byte[8]
name: parse_data
arguments: tag: D464
type_guessed: byte[8]
name: parse_data
arguments: tag: D237
type_guessed: byte[8]
name: parse_data
arguments: tag: D102
type_guessed: byte[8]
name: parse_data
arguments: tag: D425
type_guessed: byte[8]
name: parse_data
arguments: tag: D645
type_guessed: byte[8]
name: parse_data
arguments: tag: D385
type_guessed: byte[8]
name: parse_data
arguments: tag: D346
type_guessed: byte[8]
name: parse_data
arguments: tag: D619
type_guessed: byte[8]
name: parse_data
arguments: tag: D19
type_guessed: byte[8]
name: parse_data
arguments: tag: D910
type_guessed: byte[8]
name: parse_data
arguments: tag: D634
type_guessed: byte[8]
name: parse_data
arguments: tag: D28
type_guessed: byte[8]
name: parse_data
arguments: tag: D555
type_guessed: byte[8]
name: parse_data
arguments: tag: D76
type_guessed: byte[8]
name: parse_data
arguments: tag: D805
type_guessed: byte[8]
name: parse_data
arguments: tag: D301
type_guessed: byte[8]
name: parse_data
arguments: tag: D800
type_guessed: byte[8]
name: parse_data
arguments: tag: D158
type_guessed: byte[8]
name: parse_data
arguments: tag: D266
type_guessed: byte[8]
name: parse_data
arguments: tag: D857
type_guessed: byte[8]
name: parse_data
arguments: tag: D13
type_guessed: byte[8]
name: parse_data
arguments: tag: D60
type_guessed: f64
name: parse_data
arguments: tag: D316
type_guessed: byte[8]
name: parse_data
arguments: tag: D78
type_guessed: byte[8]
name: parse_data
arguments: tag: D431
type_guessed: byte[8]
name: parse_data
arguments: tag: D494
type_guessed: byte[8]
name: parse_data
arguments: tag: D501
type_guessed: byte[8]
name: parse_data
arguments: tag: D701
type_guessed: byte[8]
name: parse_data
arguments: tag: D733
type_guessed: byte[8]
name: parse_data
arguments: tag: D246
type_guessed: byte[8]
name: parse_data
arguments: tag: D232
type_guessed: byte[8]
name: parse_data
arguments: tag: D806
type_guessed: byte[8]
name: parse_data
arguments: tag: D728
type_guessed: byte[8]
name: parse_data
arguments: tag: D650
type_guessed: f64
name: parse_data
arguments: tag: D204
type_guessed: f64
name: parse_data
arguments: tag: D72
type_guessed: byte[8]
name: parse_data
arguments: tag: D742
type_guessed: byte[8]
name: parse_data
arguments: tag: D954
type_guessed: byte[8]
name: parse_data
arguments: tag: D61
type_guessed: byte[8]
name: parse_data
arguments: tag: D352
type_guessed: byte[8]
name: parse_data
arguments: tag: D882
type_guessed: byte[8]
name: parse_data
arguments: tag: D366
type_guessed: byte[8]
name: parse_data
arguments: tag: D190
type_guessed: byte[8]
name: parse_data
arguments: tag: D740
type_guessed: byte[8]
name: parse_data
arguments: tag: D162
type_guessed: byte[8]
name: parse_data
arguments: tag: D445
type_guessed: byte[8]
name: parse_data
arguments: tag: D223
type_guessed: byte[8]
name: parse_data
arguments: tag: D15
type_guessed: byte[8]
name: parse_data
arguments: tag: D618
type_guessed: byte[8]
name: parse_data
arguments: tag: D50
type_guessed: byte[8]
name: parse_data
arguments: tag: D184
type_guessed: byte[8]
name: parse_data
arguments: tag: D912
type_guessed: byte[8]
name: parse_data
arguments: tag: D405
type_guessed: byte[8]
name: parse_data
arguments: tag: D336
type_guessed: byte[8]
name: parse_data
arguments: tag: D217
type_guessed: byte[8]
name: parse_data
arguments: tag: D716
type_guessed: byte[8]
name: parse_data
arguments: tag: D363
type_guessed: byte[8]
name: parse_data
arguments: tag: D517
type_guessed: byte[8]
name: parse_data
arguments: tag: D833
type_guessed: byte[8]
name: parse_data
arguments: tag: D696
type_guessed: byte[8]
name: parse_data
arguments: tag: D731
type_guessed: byte[8]
name: parse_data
arguments: tag: D446
type_guessed: byte[8]
name: parse_data
arguments: tag: D62
type_guessed: byte[8]
name: parse_data
arguments: tag: D386
type_guessed: byte[8]
name: parse_data
arguments: tag: D714
type_guessed: byte[8]
name: parse_data
arguments: tag: D627
type_guessed: byte[8]
name: parse_data
arguments: tag: D118
type_guessed: byte[8]
name: parse_data
arguments: tag: D793
type_guessed: byte[8]
name: parse_data
arguments: tag: D828
type_guessed: byte[8]
name: parse_data
arguments: tag: D378
type_guessed: byte[8]
name: parse_data
arguments: tag: D591
type_guessed: byte[8]
name: parse_data
arguments: tag: D413
type_guessed: byte[8]
name: parse_data
arguments: tag: D609
type_guessed: byte[8]
name: parse_data
arguments: tag: D177
type_guessed: byte[8]
name: parse_data
arguments: tag: D661
type_guessed: byte[8]

tool: {"D573": [0xfc,0x2c,0x45,0x01,0x00,0x83,0x2e,0x3f]}

tool: {"D12": [0xf2,0xa0,0x4f,0x84,0xed,0x94,0x9e,0x3f]}

tool: D666: 6.698001071123802

tool: {"D508": [0x0d,0x0d,0x3e,0x7f,0x28,0x13,0xa7,0x3e]}

tool: {"D576": [0xea,0x40,0xd6,0x96,0x94,0xae,0x27,0x3f]}

tool: {"D957": [0x6e,0xb3,0xdd,0x0b,0xa2,0x41,0xcf,0x3e]}

tool: {"D717": [0xd1,0x33,0xb0,0x73,0xcd,0x84,0x36,0x3f]}

tool: {"D676": [0xb8,0x52,0x81,0xe0,0x61,0xde,0x96,0x3f]}

tool: {"D855": [0x25,0x50,0x24,0x19,0xed,0xe9,0xb3,0xbd]}

tool: {"D721": [0xda,0x54,0xdf,0x5d,0x67,0x5e,0x10,0x3e]}

tool: {"D870": [0x9b,0x60,0x15,0x69,0x6b,0xf3,0x80,0x3e]}

tool: {"D464": [0xbc,0xe6,0xbd,0x4a,0x61,0xfc,0xfc,0x3e]}

tool: {"D237": [0x0f,0x4d,0x4a,0x59,0xcf,0xce,0x7e,0x3f]}

tool: {"D102": [0xb7,0x34,0xcf,0x2a,0x41,0xfc,0x80,0xbd]}

tool: {"D425": [0x58,0xd0,0xf2,0x4f,0xfe,0x69,0x2b,0x3e]}

tool: {"D645": [0xa4,0xa8,0x06,0xd8,0x74,0x8f,0x95,0x3e]}

tool: {"D385": [0x9b,0xcc,0x5a,0x74,0xff,0xc0,0xfc,0x3e]}

tool: {"D346": [0xe8,0x94,0x78,0xf4,0xa0,0x57,0x05,0x3e]}

tool: {"D619": [0x8f,0x77,0xaa,0x37,0x2c,0xaa,0x7d,0x3e]}

tool: {"D19": [0x3e,0xd3,0xdc,0x5f,0x9b,0x35,0x09,0x3d]}

tool: {"D910": [0x18,0xe6,0x61,0x34,0xd2,0x57,0xb7,0xbd]}

tool: {"D634": [0x11,0xf7,0x4c,0x08,0xff,0xfe,0x24,0xbd]}

tool: {"D28": [0x8b,0x87,0x54,0x54,0x4b,0x95,0x87,0x3d]}

tool: {"D555": [0x61,0xf7,0x2f,0x26,0x08,0x7a,0xc9,0x3d]}

tool: {"D76": [0x57,0x27,0x46,0x6b,0x35,0x7a,0x40,0x3e]}

tool: {"D805": [0x2d,0xaf,0xa5,0xc9,0x09,0x83,0x99,0x3e]}

tool: {"D301": [0xe4,0x53,0x23,0x49,0xa0,0x51,0x01,0x3f]}

tool: {"D800": [0xf6,0x68,0xb1,0x23,0xf5,0xba,0xd6,0x3e]}

tool: {"D158": [0x40,0x56,0x29,0xd6,0xcf,0x2b,0x07,0x3e]}

tool: {"D266": [0x42,0xd1,0x39,0xf4,0x45,0xc8,0xb2,0x3e]}

tool: {"D857": [0x63,0xc6,0xe2,0xf0,0x2d,0xa3,0xf8,0x3e]}

tool: {"D13": [0xb6,0xcd,0x91,0xdc,0x8a,0xbd,0x66,0x3f]}

tool: D60: 1

tool: {"D316": [0x10,0xf7,0x4c,0x08,0xff,0xfe,0x14,0xbd]}

tool: {"D78": [0x61,0xf3,0x4c,0xa2,0x49,0x59,0xb5,0x3d]}

tool: {"D431": [0x5a,0x66,0xbb,0x13,0x58,0xc2,0xde,0x3d]}

tool: {"D494": [0x2c,0x35,0x32,0x6d,0xf1,0x75,0x91,0x3c]}

tool: {"D501": [0xeb,0xc5,0x77,0x63,0x5d,0xa0,0xd5,0x3c]}

tool: {"D701": [0x73,0x33,0x84,0xef,0x4f,0x14,0x86,0x3e]}

tool: {"D733": [0xd6,0xa6,0x84,0xcc,0x10,0xed,0xed,0x3e]}

tool: {"D246": [0xbf,0xb2,0x6b,0xaa,0x59,0xb2,0x40,0x3f]}

tool: {"D232": [0xfc,0x2d,0x58,0xb1,0x3a,0x6c,0xa4,0x3f]}

tool: {"D806": [0x1f,0x14,0xa5,0x0a,0xda,0x5c,0x53,0x3f]}

tool: {"D728": [0x8e,0x15,0x07,0xbe,0xd4,0x1d,0xa0,0x3f]}

tool: D650: 2.839940833161907

tool: D204: 999.8420897506056

tool: {"D72": [0x18,0xe6,0x61,0x34,0xd2,0x57,0xa7,0xbd]}

tool: {"D742": [0x40,0x72,0xfa,0x98,0x94,0x59,0x55,0x3e]}

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tool: {"D661": [0x2d,0x43,0x1c,0xeb,0xe2,0x36,0x1a,0x3f]}

assistant: ```c
void gsw_rho_first_derivatives(double sa, double ct, double p, double *drho_dsa, double *drho_dct, double *drho_dp) {
  double v01 = 9.998420897506056e2, v02 = 2.839940833161907e0, v03 = -3.147759265588511e-2, v04 = 1.181805545074306e-3, v05 = -6.698001071123802e0, v06 = -2.986498947203215e-2, v07 = 2.327859407479162e-4, v08 = -3.988822378968490e-2, v09 = 5.095422573880500e-4, v10 = -1.426984671633621e-5, v11 = 1.645039373682922e-7, v12 = -2.233269627352527e-2, v13 = -3.436090079851880e-4, v14 = 3.726050720345733e-6, v15 = -1.806789763745328e-4, v16 = 6.876837219536232e-7, v17 = -3.087032500374211e-7, v18 = -1.988366587925593e-8, v19 = -1.061519070296458e-11, v20 = 1.550932729220080e-10, v21 = 1.0e0, v22 = 2.775927747785646e-3, v23 = -2.349607444135925e-5, v24 = 1.119513357486743e-6, v25 = 6.743689325042773e-10, v26 = -7.521448093615448e-3, v27 = -2.764306979894411e-5, v28 = 1.262937315098546e-7, v29 = 9.527875081696435e-10, v30 = -1.811147201949891e-11, v31 = -3.303308871386421e-5, v32 = 3.801564588876298e-7, v33 = -7.672876869259043e-9, v34 = -4.634182341116144e-11, v35 = 2.681097235569143e-12, v36 = 5.419326551148740e-6, v37 = -2.742185394906099e-5, v38 = -3.212746477974189e-7, v39 = 3.191413910561627e-9, v40 = -1.931012931541776e-12, v41 = -1.105097577149576e-7, v42 = 6.211426728363857e-10, v43 = -1.119011592875110e-10, v44 = -1.941660213148725e-11, v45 = -1.864826425365600e-14, v46 = 1.119522344879478e-14, v47 = -1.200507748551599e-15, v48 = 6.057902487546866e-17, a01 = 2.839940833161907e0, a02 = -6.295518531177023e-2, a03 = 3.545416635222918e-3, a04 = -2.986498947203215e-2, a05 = 4.655718814958324e-4, a06 = 5.095422573880500e-4, a07 = -2.853969343267241e-5, a08 = 4.935118121048767e-7, a09 = -3.436090079851880e-4, a10 = 7.452101440691467e-6, a11 = 6.876837219536232e-7, a12 = -1.988366587925593e-8, a13 = -2.123038140592916e-11, a14 = 2.775927747785646e-3, a15 = -4.699214888271850e-5, a16 = 3.358540072460230e-6, a17 = 2.697475730017109e-9, a18 = -2.764306979894411e-5, a19 = 2.525874630197091e-7, a20 = 2.858362524508931e-9, a21 = -7.244588807799565e-11, a22 = 3.801564588876298e-7, a23 = -1.534575373851809e-8, a24 = -1.390254702334843e-10, a25 = 1.072438894227657e-11, a26 = -3.212746477974189e-7, a27 = 6.382827821123254e-9, a28 = -5.793038794625329e-12, a29 = 6.211426728363857e-10, a30 = -1.941660213148725e-11, a31 = -3.729652850731201e-14, a32 = 1.119522344879478e-14, a33 = 6.057902487546866e-17, b01 = -6.698001071123802e0, b02 = -2.986498947203215e-2, b03 = 2.327859407479162e-4, b04 = -5.983233568452735e-2, b05 = 7.643133860820750e-4, b06 = -2.140477007450431e-5, b07 = 2.467559060524383e-7, b08 = -1.806789763745328e-4, b09 = 6.876837219536232e-7, b10 = 1.550932729220080e-10, b11 = -7.521448093615448e-3, b12 = -2.764306979894411e-5, b13 = 1.262937315098546e-7, b14 = 9.527875081696435e-10, b15 = -1.811147201949891e-11, b16 = -4.954963307079632e-5, b17 = 5.702346883314446e-7, b18 = -1.150931530388857e-8, b19 = -6.951273511674217e-11, b20 = 4.021645853353715e-12, b21 = 1.083865310229748e-5, b22 = -1.105097577149576e-7, b23 = 6.211426728363857e-10, b24 = 1.119522344879478e-14, c01 = -2.233269627352527e-2, c02 = -3.436090079851880e-4, c03 = 3.726050720345733e-6, c04 = -1.806789763745328e-4, c05 = 6.876837219536232e-7, c06 = -6.174065000748422e-7, c07 = -3.976733175851186e-8, c08 = -2.123038140592916e-11, c09 = 3.101865458440160e-10, c10 = -2.742185394906099e-5, c11 = -3.212746477974189e-7, c12 = 3.191413910561627e-9, c13 = -1.931012931541776e-12, c14 = -1.105097577149576e-7, c15 = 6.211426728363857e-10, c16 = -2.238023185750219e-10, c17 = -3.883320426297450e-11, c18 = -3.729652850731201e-14, c19 = 2.239044689758956e-14, c20 = -3.601523245654798e-15, c21 = 1.817370746264060e-16, pa2db = 1e-4;
  double sqrtsa, v_hat_denominator, v_hat_numerator;
  double dvhatden_dct, dvhatnum_dct, dvhatden_dsa, dvhatnum_dsa;
  double dvhatden_dp, dvhatnum_dp, rho, rec_num;
  sqrtsa = sqrt(sa);
  v_hat_denominator = v01 + ct * (v02 + ct * (v03 + v04 * ct)) + sa * (v05 + ct * (v06 + v07 * ct) + sqrtsa * (v08 + ct * (v09 + ct * (v10 + v11 * ct)))) + p * (v12 + ct * (v13 + v14 * ct) + sa * (v15 + v16 * ct) + p * (v17 + ct * (v18 + v19 * ct) + v20 * sa));
  v_hat_numerator = v21 + ct * (v22 + ct * (v23 + ct * (v24 + v25 * ct))) + sa * (v26 + ct * (v27 + ct * (v28 + ct * (v29 + v30 * ct))) + v36 * sa + sqrtsa * (v31 + ct * (v32 + ct * (v33 + ct * (v34 + v35 * ct))))) + p * (v37 + ct * (v38 + ct * (v39 + v40 * ct)) + sa * (v41 + v42 * ct) + p * (v43 + ct * (v44 + v45 * ct + v46 * sa) + p * (v47 + v48 * ct)));
  dvhatden_dct = a01 + ct * (a02 + a03 * ct) + sa * (a04 + a05 * ct + sqrtsa * (a06 + ct * (a07 + a08 * ct))) + p * (a09 + a10 * ct + a11 * sa + p * (a12 + a13 * ct));
  dvhatnum_dct = a14 + ct * (a15 + ct * (a16 + a17 * ct)) + sa * (a18 + ct * (a19 + ct * (a20 + a21 * ct)) + sqrtsa * (a22 + ct * (a23 + ct * (a24 + a25 * ct)))) + p * (a26 + ct * (a27 + a28 * ct) + a29 * sa + p * (a30 + a31 * ct + a32 * sa + a33 * p));
  dvhatden_dsa = b01 + ct * (b02 + b03 * ct) + sqrtsa * (b04 + ct * (b05 + ct * (b06 + b07 * ct))) + p * (b08 + b09 * ct + b10 * p);
  dvhatnum_dsa = b11 + ct * (b12 + ct * (b13 + ct * (b14 + b15 * ct))) + sqrtsa * (b16 + ct * (b17 + ct * (b18 + ct * (b19 + b20 * ct)))) + b21 * sa + p * (b22 + ct * (b23 + b24 * p));
  dvhatden_dp = c01 + ct * (c02 + c03 * ct) + sa * (c04 + c05 * ct) + p * (c06 + ct * (c07 + c08 * ct) + c09 * sa);
  dvhatnum_dp = c10 + ct * (c11 + ct * (c12 + c13 * ct)) + sa * (c14 + c15 * ct) + p * (c16 + ct * (c17 + c18 * ct + c19 * sa) + p * (c20 + c21 * ct));
  rec_num = 1e0 / v_hat_numerator;
  rho = rec_num * v_hat_denominator;
  *drho_dsa = (dvhatden_dsa - dvhatnum_dsa * rho) * rec_num;
  *drho_dct = (dvhatden_dct - dvhatnum_dct * rho) * rec_num;
  *drho_dp = pa2db * (dvhatden_dp - dvhatnum_dp * rho) * rec_num;
  return;
}
```