Details

simplify1.0hr

Calls

28442 calls:

Slowest
2.3s
(* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))
2.2s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))))
2.1s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J)))))
2.0s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))))
2.0s
(* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))))

prune5.7m

rewrite4.9m

Algorithm
87×rewrite-expression-head
Calls

338 calls:

Slowest
44.1s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
18.3s
(* (* J (+ (* l (+ (log (exp (* l (* 1/3 l)))) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
11.5s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J))))
11.1s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J))
8.3s
(* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2)))
Rules
3119808×times-frac
1487253×add-sqr-sqrt
1250498×*-un-lft-identity
1230581×add-cube-cbrt
277091×associate-/r/
263572×associate-*l*
261410×associate-*r*
244609×swap-sqr
236975×frac-times
181024×associate-/l*
170505×associate-/r*
127479×div-inv
90540×unswap-sqr
55483×clear-num
52766×frac-2neg
37496×tan-quot
29829×associate-*r/
29202×associate-*l/
21970×*-commutative
19403×sqrt-prod
15909×sqrt-div
12004×cbrt-prod
9341×frac-add
8824×associate-/l/
6620×distribute-lft-out
5459×un-div-inv
4941×unpow-prod-down
4662×flip3-- flip--
4240×flip-+ flip3-+
4057×difference-of-squares
3938×add-exp-log
3274×add-cbrt-cube
1418×prod-exp
1402×frac-sub
1380×div-exp
1255×sqr-pow
1208×cbrt-unprod
1152×pow1
1114×cbrt-undiv
887×distribute-lft-out--
634×sin-mult
545×cbrt-div
382×add-log-exp
360×pow-prod-down
338×insert-posit16
276×rem-sqrt-square
186×pow-exp
145×pow-unpow
108×distribute-rgt-in distribute-lft-in
90×difference-of-sqr-1
87×pow-to-exp
86×sqrt-pow1
70×pow1/2
69×log-pow
63×unpow2 sub-neg
56×exp-prod
52×+-commutative
50×1-exp rec-exp
46×pow-prod-up
41×pow1/3
32×associate-+l+ div-sub
28×distribute-lft-neg-in distribute-rgt-neg-in
24×pow-pow pow-sqr
23×pow-sub
22×associate-+r+ pow-plus
19×pow2
16×distribute-rgt-out--
14×associate--l+
13×distribute-rgt-out
11×sum-log diff-log
log-prod
sqr-sin
sub-div
pow-flip distribute-lft1-in remove-double-div pow3 cos-sum rem-log-exp
inv-pow
associate--r+ neg-mul-1 acos-asin
associate-+r- cos-diff
exp-to-pow distribute-neg-frac asin-acos e-exp-1
neg-sub0 remove-posit16 sqrt-undiv distribute-frac-neg associate--l- sqrt-pow2 associate-+l- unpow1/3

sample2.1m

Algorithm
44×intervals
Results
31.5s149476×body80valid
27.1s15788×body1280valid
18.7s8132×body10240exit
15.6s12326×body640valid
10.2s49890×body80nan
6.0s6222×body320valid
3.9s7670×body160valid
3.8s3188×body2560valid
622.0ms563×body1280nan
560.0ms657×body640nan
303.0ms87×body5120valid
204.0ms336×body320nan
149.0ms207×body160nan

series1.9m

Calls

338 calls:

Slowest
28.1s
(sqrt (* (* (cbrt (* 2 n)) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
15.5s
(sqrt (* (cbrt (* (cbrt (* 2 n)) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
15.2s
(sqrt (* (cbrt (* (cbrt (* 2 n)) U)) (- (- t (* (/ l (/ Om l)) 2)) (* (* (* (/ l Om) (/ l Om)) n) (- U U*)))))
1.6s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.5s
(* (* (cbrt (* 2 n)) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))

regimes16.0s

Accuracy

Total 14.1b remaining (41.1%)

8.6b68%Toniolo and Linder, Equation (7)
2.0b0%Toniolo and Linder, Equation (3b), real
1.6b0%Henrywood and Agarwal, Equation (3)
0.4b0%Maksimov and Kolovsky, Equation (4)
0.4b0%Migdal et al, Equation (64)

localize4.2s

bsearch853.0ms

end1.0ms