qr{
(?(DEFINE)
    (?<expr>
        (?&number)
        (?:
            \s+
            (?:
                (?&number)
            |   (?&unary_op)
            |   (?&binary_op)
            )
        )*
    )
    (?<number>
        ( \d+ (?: [.] \d* )? | [.] \d+ )
        (?{ local @stack = ( @stack, $^N ) })
    )
    (?<unary_op>
        ( chs | abs | sqr | sqrt | sin | cos | tan )
        (?(?{ @stack < 1 }) (*FAIL) )
        (?{ local @stack = @stack; $operators{$^N}->($stack[-1]) })
    )
    (?<binary_op>
        ( [-+/*^] )
        (?(?{ @stack < 2 }) (*FAIL) )
        (?{ local @stack = @stack; $operators{$^N}->($stack[-2], pop @stack) })
    )
)

    \A \s* (?&expr) \s* \z
    (?(?{ @stack != 1 }) (*FAIL) )
    (?{ $result = $stack[0] })
    |
    (?{ $result = undef }) (*FAIL)

}msx