qr{
(?(DEFINE)
    (?<expr>
        (?&number)
    |   (?&expr) \s+ (&unary_op)
    |   (?&expr) \s+ (?&expr) \s+ (&binary_op)
    )
    (?<number>
        \d+ (?: [.] \d* )?
    |   [.] \d+
    )
    (?<unary_op>
        (?: chs | abs | sqr | sqrt | sin | cos | tan )
    )
    (?<binary_op>
        [-+/*^]
    )
)
    \A \s* (?&expr) \s* \z
}msx;