Assembly floating point math

I am making a compiler that compiles to x86_64 assembly, and I am trying to implement floating point math. However, I soon ran into problems because floating points are a struggle in assembly, so I am trying to practice with them, but I am finding no luck.

In this program, I want to add two floats together, compare them with another float and print a message if they are equal, but nothing is being printed.

section .data
	float1: dd 3.14
	float2: dd 5.72
	cmp_float: dd 8.86
	msg: db "Is equal!", 10, 0
	msg_len equ $-msg

section .bss
	result: resd 1

section .text
	global _start

_start:
	fld dword [float1]  ; Load float1 into FPU stack
	fld dword [float2]  ; Load float2 into FPU stack
	faddp               ; Add two top floats of the FPU stack and push back onto the FPU stack

	fcomp dword [cmp_float] ; Compare with the top value of the FPU stack

    fstsw ax            ; Store FPU status word in AX register
    sahf                ; Move AH register to FLAGS register

	je .equal
	jmp .exit
.equal:
	mov rax, 1
	mov rdi, 1
	mov rsi, msg
	mov rdx, msg_len
	syscall
.exit:
	mov rax, 60
	mov rdi, 0
	syscall

I didn't know about x87 and everything, thank you @Jester, instead use SIMD (Single Instruction, Multiple Data) instructions provided by the SSE (Streaming SIMD Extensions) or AVX (Advanced Vector Extensions) instruction sets:

section .data
    number1 dd 2.5          ; First floating-point number
    number2 dd 1.3          ; Second floating-point number
    result_add dd 0.0       ; Variable to store the addition result
    result_sub dd 0.0       ; Variable to store the subtraction result
    result_mul dd 0.0       ; Variable to store the multiplication result
    result_div dd 0.0       ; Variable to store the division result

section .text
    global _start

_start:
    ; Addition
    movss xmm0, [number1]       ; Load number1 into xmm0
    movss xmm1, [number2]       ; Load number2 into xmm1
    addss xmm0, xmm1             ; Add xmm1 to xmm0
    movss [result_add], xmm0    ; Store the result

    ; Subtraction
    movss xmm0, [number1]       ; Load number1 into xmm0
    movss xmm1, [number2]       ; Load number2 into xmm1
    subss xmm0, xmm1             ; Subtract xmm1 from xmm0
    movss [result_sub], xmm0    ; Store the result

    ; Multiplication
    movss xmm0, [number1]       ; Load number1 into xmm0
    movss xmm1, [number2]       ; Load number2 into xmm1
    mulss xmm0, xmm1             ; Multiply xmm0 by xmm1
    movss [result_mul], xmm0    ; Store the result

    ; Division
    movss xmm0, [number1]       ; Load number1 into xmm0
    movss xmm1, [number2]       ; Load number2 into xmm1
    divss xmm0, xmm1             ; Divide xmm0 by xmm1
    movss [result_div], xmm0    ; Store the result

    ; ... Rest of your code

    ; Exit the program
    mov rax, 60
    mov rdi, 0
    syscall