plus0yyplussxysplusxytimes0y0timessxyplusytimesxyeq_nat0syfalseeq_nat00trueeq_natsxsyeq_natxyeq_natsx0falseeq_ratpairabpaircdeq_nattimesadtimesbcdiv_ratpairabpaircdpairtimesadtimesbctimes_ratpairabpaircdpairtimesactimesbdplus_ratpairabpaircdpairplustimesadtimescbtimesbdnon_zero_ratpairabnon_zero_nattimesabnon_zero_nats0truenon_zero_nat0falsenon_zero_natssxnon_zero_natsx2pairss0s0minus_natsxsyminus_natxysqrt2rif_approxnon_zero_ratreq_rat2times_ratrrrif_approxtruetruerrif_approxtruefalsersqrt2div_ratplus_ratrdiv_rat2r2initsqrt22run_againxrun_againinitplus200s1times2eq_nat2false0true0eq_rat2pair2div_rat2times_rat2plus_rat2non_zero_rat1non_zero_nat120minus_nat2sqrt21if_approx3init0run_again1INNERMOST