Chaining results using match can get pretty untidy; luckily, the ? operator can be used to make things pretty again. ? is used at the end of an expression returning a Result, and is equivalent to a match expression, where the Err(err) branch expands to an early Err(From::from(err)), and the Ok(ok) branch expands to an ok expression.

mod checked {
    #[derive(Debug)]
    enum MathError {
        DivisionByZero,
        NonPositiveLogarithm,
        NegativeSquareRoot,
    }

    type MathResult = Result<f64, MathError>;

    fn div(x: f64, y: f64) -> MathResult {
        if y == 0.0 {
            Err(MathError::DivisionByZero)
        } else {
            Ok(x / y)
        }
    }

    fn sqrt(x: f64) -> MathResult {
        if x < 0.0 {
            Err(MathError::NegativeSquareRoot)
        } else {
            Ok(x.sqrt())
        }
    }

    fn ln(x: f64) -> MathResult {
        if x <= 0.0 {
            Err(MathError::NonPositiveLogarithm)
        } else {
            Ok(x.ln())
        }
    }

    // Intermediate function
    fn op_(x: f64, y: f64) -> MathResult {
        // if `div` "fails", then `DivisionByZero` will be `return`ed
        let ratio = div(x, y)?;

        // if `ln` "fails", then `NonPositiveLogarithm` will be `return`ed
        let ln = ln(ratio)?;

        sqrt(ln)
    }

    pub fn op(x: f64, y: f64) {
        match op_(x, y) {
            Err(why) => panic!(match why {
                MathError::NonPositiveLogarithm
                    => "logarithm of non-positive number",
                MathError::DivisionByZero
                    => "division by zero",
                MathError::NegativeSquareRoot
                    => "square root of negative number",
            }),
            Ok(value) => println!("{}", value),
        }
    }
}

fn main() {
    checked::op(1.0, 10.0);
}

Be sure to check the documentation, as there are many methods to map/compose Result.