Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

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1 \begin{tikzpicture}[font=\sffamily\small]
2 \node[anchor=west] at (0,3.2) {actual error sum\quad versus\quad ceiling envelope};
3 \draw[->] (0,0)--(8,0) node[right] {error};
4 \foreach \x/\v in {0/0,2/{1/10},4/{1/5}}{\draw (\x,0)--(\x,-.1);\node[below] at (\x,-.1) {$\v$};}
5 \draw[dotted] (2,0)--(2,2.2);\node[above] at (2,2.2) {budget};
6 \draw[very thick] (0,1.6)--(2.8,1.6);\fill (2.8,1.6) circle (2pt);
7 \node[right] at (4.3,1.6) {$7/50>1/10$};
8 \draw[very thick] (0,.8)--(1.6,.8);\fill (1.6,.8) circle (2pt);
9 \node[right] at (4.3,.8) {$2/25\le1/10$};
10 \draw[thick,dashed] (0,1.3)--(4,1.3);\draw[thick,dashed] (0,.5)--(4,.5);
11 \node[anchor=west] at (0,-1.1) {Both ceiling envelopes are $h(1+1)=1/5$.};
12 \end{tikzpicture}

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