qr{
    \A \s*
    (?<start_number> \d+ (?: [.] \d* )? | [.] \d+ )
    (?{ 1 })
    (?>
        \s+
        (?:
            (?<number> \d+ (?: [.] \d* )? | [.] \d+ )
            (?{ $^R + 1})
        |
            (?<unary_op> chs | abs | sqrt | sqr | sin | cos | tan )
        |
            (?<binary_op> [-+/*^] )
            (?{ $^R - 1 })
        )
    )*
    \s* \z
    (?(?{ $^R != 1 }) (*FAIL) )
}msx,