FMFT-Fully Massive Four-loop Tadpoles 
FMFT is a FORM package for reduction fully masive four-loop tadpole integrals to set of master integrals. For correct operation FMFT needs last development version of FORM or at least FORM version 4 available as precompiled binary.
If you use these software, please cite corresponding CPC paper:
FMFT: Fully Massive Four-loop Tadpoles By Andrey Pikelner
Basic topologies
Input and examples
For input we use d1,...,d10 as massive denominators according to
topologies H and X defined as d_i=p_i^2-m^2, and mass is set
equal to one.
#-
#include fmft.hh
L ex = p2.p3*p2.p2/d1^-2/d2^2/d3^0/d4^1/d5^1/d6^1/d7^1/d8^1/d9^3/d10^0;
#call fmft
#call exp4d(1)
b ep;
Print+s;
.end
Speed tests
To compare with C++ version of FIRE package used with rules generated by LiteRed we calculate following integral:
L ex = d1^`N'/d2/d3/d4/d5/d6/d7/d8/d9/d10
Execution time present for different powers of numerator. FIRE
used in #memory mode with 8 cores and FMFT run with parallel
version of FORM with 8 workers tform -w8. Time format is
hh:mm:ss
| N | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|
| FMFT | 0:00:11 | 0:00:27 | 0:01:55 | 0:07:35 | 0:25:31 | 01:30:31 |
| FIRE | 0:01:58 | 0:09:10 | 0:28:17 | 2:16:42 | 9:19:57 | 46:42:29 |