Details

sample2.3m (45.8%)

Algorithm
21×intervals
Results
1.3m39409×body10240exit
13.0s7146×body1280valid
12.0s57664×body80nan
10.9s56793×body80valid
8.0s3450×body2560valid
5.9s4683×body640valid
1.5s2305×body320valid
539.0ms29×body5120valid
472.0ms1198×body160valid
280.0ms8356×pre80true
29.0ms22×body2560nan
20.0ms29×body1280nan
16.0msbody5120nan
9.0ms15×body640nan
5.0ms11×body320nan
1.0msbody160nan

simplify1.8m (36.1%)

prune27.2s (9.1%)

series21.1s (7.1%)

Calls

92 calls:

2.5s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.4s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
2.4s
(sqrt (* (* U 2) (* n (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))))
2.4s
(sqrt (* (* (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
2.3s
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))

regimes3.1s (1.0%)

Accuracy

Total 11.4b remaining (5.3%)

Threshold costs 1.8b (0.8%)

8.0b29.9%Toniolo and Linder, Equation (13)
1.7b0%Random Jason Timeout Test 004
0.9b0%Random Jason Timeout Test 012
0.8b0%Random Jason Timeout Test 006
0.0b0%Random Jason Timeout Test 002

localize1.1s (0.4%)

rewrite1.1s (0.4%)

Algorithm
27×rewrite-expression-head
Calls

92 calls:

101.0ms
(sqrt (* (* (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))) (cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))))
80.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
75.0ms
(* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t)))
70.0ms
(sqrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
59.0ms
(cbrt (* (* (* U 2) n) (fma (- U* U) (/ (/ n (/ Om l)) (/ Om l)) (fma (/ l (/ Om l)) -2 t))))
Rules
360×add-sqr-sqrt
342×*-un-lft-identity
329×pow1
306×add-cube-cbrt
175×times-frac
168×add-exp-log
153×add-cbrt-cube
108×sqrt-pow1
94×expm1-log1p-u log1p-expm1-u
92×add-log-exp
89×unpow-prod-up
82×log-pow
79×pow-prod-down
72×prod-diff
69×exp-prod
59×pow-pow
51×unpow-prod-down
49×pow1/2
48×pow-unpow
47×sqrt-prod
46×cbrt-prod
45×pow-prod-up
39×pow1/3
35×prod-exp
33×cbrt-unprod
31×associate-/r*
26×log-prod
23×pow-plus pow-sqr
22×associate-*r*
18×distribute-lft-out-- difference-of-squares
14×fma-udef
12×associate-*l* pow-exp
11×pow2 sqr-pow div-inv associate-/l*
pow-to-exp
sub-neg rem-sqrt-square
div-exp cbrt-undiv distribute-lft-in distribute-rgt-in *-commutative
rem-log-exp sin-sum unswap-sqr sqrt-pow2 swap-sqr pow-sub
associate-/r/
expm1-udef frac-2neg pow3 clear-num
sinh-def expm1-log1p associate-/l/ flip3-- flip-- log1p-expm1 acos-asin sqrt-unprod log1p-udef
div-sub rem-exp-log exp-sum cosh-def sin-diff e-exp-1

bsearch556.0ms (0.2%)

end0.0ms (0.0%)