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Many cutting-edge physics calculations hit a brick wall — not for lack of ideas, but because of arithmetic. We're talking about integrals that express particle collision probabilities or the shape of gravitational wave bursts. To get a number, these integrals need to be simplified — reduced to a handful of "master integrals," much like a multiplication table. The procedure is known: Laporta's algorithm systematically iterates through combinations until only the basic building blocks remain. The trouble is that for complex problems, the number of such combinations grows faster than a snowball, like a high-degree polynomial. The calculation chokes.

The authors of the new work decided not to iterate through everything, but to dig a tunnel. They trained a program to search for a sparse chain of intermediate integrals — a kind of zigzag trajectory that connects the original unwieldy integral to the master integrals. This chain resembles a thin tube: inside it, there are few steps, and their number grows not avalanche-like but smoothly, almost like a straight line. They named this strategy "tubular seeding."

The method was tested on real problems. First, they took a monster single integral: nonplanar, two-loop, with five lines and a 20th power in the numerator. The usual approach fails here — the enumeration balloons sky-high. "Tubular seeding" performed the reduction in acceptable time on a regular machine. Then they split a whole set of rank-10 integrals into parts, and again won in speed and memory compared to other modern methods. This opens the door to practical calculations, for example, for analyzing data from gravitational wave detectors.

So calculations that once required clusters become feasible on a laptop. Physicists gain a tool to test theories faster and process signals from space.