Details

simplify47.1m

Calls

16995 calls:

Slowest
3.0s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w D) (* w D)) (* w D)))) (* (* h h) h))
2.9s
(/ (* (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d d) d) (* (* c0 c0) c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
2.9s
(* (* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (/ (* h h) (* (* 1 1) 1))) (/ h (* (* l l) l)))
2.8s
(/ (* (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D))) (/ (* (* (* d c0) (* d c0)) (* d c0)) (* (* (* w w) w) (* (* D D) D)))) (* (* h h) h))
2.8s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))

prune5.1m

sample3.3m

Algorithm
54×intervals
Results
53.3s240021×body80valid
38.2s160937×body80nan
29.1s18270×body1280valid
19.3s8525×body10240exit
19.1s14417×body640valid
7.0s5006×body2560valid
6.8s7049×body320valid
6.1s2363×body5120valid
4.9s7921×body160valid
651.0ms614×body1280nan
409.0ms552×body640nan
195.0ms339×body320nan
115.0ms177×body160nan

series1.2m

Calls

407 calls:

Slowest
2.2s
(sqrt (* 2 (* (* U n) (- (- t (* (/ (* l l) Om) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
2.2s
(sqrt (* 2 (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
2.2s
(sqrt (* 2 (* (sqrt (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))) (sqrt (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))))
2.1s
(sqrt (* 2 (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))
2.1s
(sqrt (* 2 (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))

rewrite40.7s

Algorithm
104×rewrite-expression-head
Calls

407 calls:

Slowest
9.8s
(* (* (* (* (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))) (sqrt (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))) -2) (cos (/ K 2))) J)
4.2s
(* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l))
1.4s
(/ (* (* -1/2 (* (* (/ D d) (/ M 2)) (* (* (/ D d) (/ M 2)) h))) (* (sqrt (/ (cbrt d) (cbrt h))) (fabs (/ (cbrt d) (cbrt h))))) l)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
923.0ms
(sqrt (* 2 (* (sqrt (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))) (sqrt (* (* U n) (- (- t (* (/ l (/ Om l)) 2)) (* (* n (* (/ l Om) (/ l Om))) (- U U*))))))))
Rules
26343×times-frac
13412×add-sqr-sqrt
12145×*-un-lft-identity
11455×add-cube-cbrt
10828×add-exp-log
8112×add-cbrt-cube
6332×sqrt-prod
5265×prod-exp
4611×associate-*r/
3923×cbrt-unprod
3428×div-exp
2585×cbrt-undiv
2579×sqrt-div
2287×pow1
2154×frac-times
1421×associate-*r*
1368×frac-sub
1364×flip3-- flip--
1252×associate-*l/
1145×div-inv
1094×associate-/r/
982×associate-/l*
947×associate-*l*
794×pow-prod-down
588×associate-/r*
519×unswap-sqr
467×add-log-exp
407×insert-posit16
339×flip-+ flip3-+
327×pow-unpow
291×pow-exp
245×pow-prod-up
238×1-exp
210×unpow-prod-down
179×*-commutative
170×difference-of-squares
141×pow-sqr
140×pow-plus
135×distribute-lft-out
130×swap-sqr
129×pow-to-exp
123×cbrt-prod
118×rec-exp distribute-lft-out--
114×tan-quot
102×frac-2neg clear-num
94×sqrt-pow1 sqr-pow
85×pow2
81×distribute-rgt-in associate-/l/ distribute-lft-in
76×sin-mult
71×sub-neg
70×frac-add
60×distribute-rgt-neg-in
59×pow1/2
56×distribute-lft-neg-in distribute-rgt-out--
52×pow-pow
44×rem-sqrt-square
35×cbrt-div
29×pow-flip
28×pow1/3
24×associate--l+
23×inv-pow div-sub diff-log
13×pow-sub
sum-log +-commutative
associate--r+ neg-mul-1 sqr-sin un-div-inv
associate-+l+ cos-sum unpow2
pow3
rem-cube-cbrt remove-posit16 neg-sub0 neg-log difference-of-sqr-1 distribute-neg-frac asin-acos acos-asin
log-prod cube-unmult associate--l- log-pow cos-diff
cube-prod associate-+r- associate-+r+ distribute-frac-neg unpow3 sub-div cube-mult associate--r-
cos-mult sqrt-pow2 exp-to-pow unpow1/3 sqr-cos rem-cbrt-cube exp-prod rem-log-exp

regimes17.4s

Accuracy

Total 55.5b remaining (33.7%)

11.2b-1.6%Henrywood and Agarwal, Equation (13)
10.7b30%Henrywood and Agarwal, Equation (3)
8.2b7.5%Maksimov and Kolovsky, Equation (3)
6.6b10%Henrywood and Agarwal, Equation (12)
6.2b28.9%Toniolo and Linder, Equation (13)

localize5.6s

bsearch3.4s

end1.0ms