Current size is 240 bytes. If we use eval, we can cut it down to 164 bytes:

function(i,s,t,j,e){i=i.split(' ');t=[];t.o=t.pop;t.u=t.push;for(j=0;j<i.length;j++){e=i[j];/[\d]+/.test(e)?t.u(e*1):eval('s=t.o(),t.u(t.o()'+e+'s)')};return t[0];}

I'll quote @140bytes on eval: "avoid it if you can, but sometimes ya gotta do what ya gotta do."

Is it possible to remove 100 bytes, or should we aim for the extra 24 bytes in the eval version?

Maybe start with removing useless parenthesis, semi-colons and apply other common tricks...

Please do! I honestly thought I had to keep those semi-colons at least...

Edit: Ah, there's was one at the end.

But I see I left a space by mistake. I'll remove that one.

In each case you pop 2 values from the stack. I guess you could cut some bits doing it only once at the beginning of the loop. A while(j--) loop could be shorter (but reversed). There's a lot of extra parenthesis and some semi-colons. The ternary operator (?:) is shorter than &&||.
Have fun!

function(i,s,t,j,e){i=i.split(' ');t=[];t.o=t.pop;t.u=t.push;for(j=0;e=i[j++];)+e==e?t.u(e*1):eval('s=t.o(),t.u(t.o()'+e+'s)');return t[0]}

function(a,b){b=[];a.replace(/\S+/g,function(c){b.push(+c==c?c:eval((a=b.pop(),b.pop())+c+a))});return b[0]}

Optional illustrative image

That's more like it. Well done :)

Yay! @tobeytailor got it to just under tweet-size! Then @subzey cut it down/reimplemented it to 108 bytes! I'll be updating.

Save some bytes.

function(a,b){return(b=[])[a.replace(/\S+/g,function(c){b.push(+c==c?c:eval(b.pop(a=b.pop())+c+a))}),0]}

Great! I will update later. (Edit: done)

If 0 wasn't allowed as an operand, we could shorten it to

function(a,b){return(b=[])[a.replace(/\S+/g,function(c){b.push(+c||eval(b.pop(a=b.pop())+c+a))}),0]}

But it is...

Using the ideas outlined above, the eval-less version now is under 140 bytes too (138 bytes):

function(a,b){return(b=[])[a.replace(/\S+/g,function(c,d){b.push(+c==c?+c:(d=b.pop(a=b.pop()),c=='+'?d+a:c=='-'?d-a:c=='*'?d*a:d/a))}),0]}

Thanks everyone.

Save 2 bytes.

function(a,b){return(b=[])[a.replace(/\S+/g,function(c,d){b.push(+c==c?+c:{'+':(d=b.pop(a=b.pop()))+a,'-':d-a,'*':d*a,'/':d/a}[c])}),0]}

or this

function(a,b){return(b=[])[a.replace(/\S+/g,function(c,d){b.push(+c==c?+c:[(d=b.pop(a=b.pop()))+a,d-a,d*a,d/a]['+-*/'.indexOf(c)])}),0]}

I'm learning something in every comment. Great work, @tsaniel!

With ES6 you can

• Lift d variable to the top so you can ignore one (, )
  With the use of => function you can also remove all return and make one liner by omitting {} that makes it return the first thing

(a,b,d)=>(b=[])[a.replace(/\S+/g,c=>b.push(+c==c?+c:{'+':(d=b.pop(a=b.pop()))+a,'-':d-a,'*':d*a,'/':d/a}[c])),0]