float32(Rat.Float64(x)) is not the same as Rat.Float32(x) in general (adjusted for
correct arguments, etc.):

package main

import (
    "fmt"
    "math/big"
)

func main() {
    const x = 340282356779733661637539395458142568447
    fmt.Println(float64(x), float32(x))
    z, ok := new(big.Rat).SetString("340282356779733661637539395458142568447")
    if !ok {
        panic("SetString failed")
    }
    t, _ := z.Float64()
    fmt.Println(t, float32(t))
}

produces:

3.4028235677973366e+38 3.4028235e+38
3.4028235677973366e+38 +Inf

i.e., we need a Rat.Float32 implementation with correct rounding for 32bit floats.