Details

simplify3.2m

Calls

1126 calls:

Slowest
1.3s
(* (* (* (* 2 n) (* 2 n)) (* 2 n)) (* (* (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))))
1.2s
(* (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2))) (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2))) (* (* (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))) (/ (cbrt l) (cbrt Om))) (/ l Om))) (* (* (- U U*) (- U U*)) (- U U*)))
1.2s
(* (* (* (* 2 2) 2) (* (* n n) n)) (* (* (* U U) U) (* (* (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))))
1.1s
(* (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))))) (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))))) (* (* (- U U*) (- U U*)) (- U U*)))
1.1s
(* (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))))) (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))))) (* (* (- U U*) (- U U*)) (- U U*)))

sample1.4m

Algorithm
12×intervals
Results
52.4s32487×body10240exit
8.2s3524×body2560valid
6.4s37151×body80valid
5.2s5028×body1280valid
5.2s37305×body80nan
1.8s2898×body640valid
753.0ms8256×pre80true
687.0ms1447×body320valid
608.0ms733×body160valid
28.0ms15×body5120valid
14.0msbody5120nan
10.0ms11×body1280nan
8.0msbody2560nan
6.0msbody640nan
3.0ms11×body160nan
2.0msbody320nan

prune21.2s

series9.5s

Calls

60 calls:

Slowest
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.1s
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))))
1.1s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))))
576.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))

regimes2.7s

Accuracy

Total 10.9b remaining (6%)

10.5b20.3%Toniolo and Linder, Equation (13)
0.2b0%Random Jason Timeout Test 004
0.2b0%Random Jason Timeout Test 012
0.0b0%Random Jason Timeout Test 002
0.0b0%Random Jason Timeout Test 014

rewrite1.8s

Algorithm
19×rewrite-expression-head
Calls

60 calls:

Slowest
200.0ms
(* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))))
176.0ms
(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))
176.0ms
(* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))
160.0ms
(sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))))
147.0ms
(* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))
Rules
718×add-exp-log
417×prod-exp
342×associate-*r/
257×add-sqr-sqrt
228×pow1
224×*-un-lft-identity
214×add-cbrt-cube
192×add-cube-cbrt
132×prod-diff
118×div-exp
114×cbrt-unprod distribute-rgt-in distribute-lft-in
112×frac-times flip3-- flip--
104×frac-sub
86×associate-*r*
82×associate-*l/
76×pow-prod-down
66×pow-exp
60×sinh-def add-log-exp expm1-log1p-u insert-posit16 sqrt-div log1p-expm1-u
50×associate--l+
42×times-frac
31×associate-*l*
29×unpow-prod-down
28×sub-neg
24×log-prod sqrt-pow1 log-pow
21×unswap-sqr
19×exp-prod cbrt-undiv
17×*-commutative
16×distribute-lft-out-- difference-of-squares
15×pow-to-exp
14×pow-prod-up cbrt-div pow-plus
13×sqrt-prod
associate-/r*
rem-log-exp unpow2 associate-/l* pow2 sqr-pow swap-sqr pow-sqr
pow1/2 div-inv
pow3 fma-udef
exp-sum acos-asin
pow1/3 associate-/l/ frac-2neg associate-/r/ clear-num rem-cbrt-cube cbrt-prod cosh-def
div-sub rem-exp-log

localize697.0ms

bsearch542.0ms

end0.0ms