Details

simplify34.2m

Calls

12220 calls:

Slowest
2.7s
(* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l)))
2.6s
(* (* (/ (* (* (* 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)))
2.4s
(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))
2.4s
(* (/ (* (* 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)))))
2.4s
(* (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l)))

prune3.7m

sample3.3m

Algorithm
53×intervals
Results
53.0s231554×body80valid
39.9s151542×body80nan
31.1s17770×body1280valid
18.1s8633×body10240exit
17.6s14204×body640valid
6.9s5048×body2560valid
6.2s2363×body5120valid
6.0s7154×body320valid
3.7s7798×body160valid
830.0ms595×body640nan
676.0ms622×body1280nan
475.0ms197×body160nan
301.0ms380×body320nan

series1.2m

Calls

406 calls:

Slowest
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1)))
1.6s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite31.6s

Algorithm
105×rewrite-expression-head
Calls

406 calls:

Slowest
1.6s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J))
1.5s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.4s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
1.3s
(exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))
Rules
32769×times-frac
15453×*-un-lft-identity
14710×add-sqr-sqrt
13800×add-cube-cbrt
8437×sqrt-prod
6123×add-exp-log
4413×add-cbrt-cube
2398×prod-exp
2148×div-exp
1609×associate-/r/
1571×cbrt-unprod
1560×cbrt-undiv
1420×pow1
1409×div-inv
926×associate-/l*
853×associate-*r/
842×distribute-rgt-out--
796×sqrt-div
766×pow-unpow
727×associate-*l*
700×associate-/r*
587×associate-*r*
527×add-log-exp
517×associate-*l/
504×flip-+ flip3-+
499×frac-times
453×pow-prod-down
446×flip3-- flip--
405×insert-posit16
370×cbrt-prod
357×difference-of-squares
298×frac-add
282×pow-exp
253×distribute-lft-out--
214×unpow-prod-down
177×unswap-sqr
158×exp-prod
145×cbrt-div
143×1-exp
134×distribute-lft-out *-commutative
126×tan-quot
122×rec-exp
121×pow-to-exp
112×distribute-rgt-neg-in
107×sqrt-pow1
98×distribute-lft-neg-in frac-2neg clear-num
93×sqr-pow
92×swap-sqr
83×pow1/2
75×pow-prod-up
66×sin-mult rem-sqrt-square
55×pow1/3
54×distribute-rgt-in distribute-lft-in
52×sub-neg
47×diff-log
44×pow-sqr
42×pow-plus
41×pow-pow associate-/l/
31×pow2
30×div-sub
27×log-pow
22×rem-exp-log
21×log-prod
18×pow-flip frac-sub
16×sum-log difference-of-sqr-1
15×exp-sum
14×neg-log inv-pow neg-mul-1
13×pow-sub
12×+-commutative
10×unpow2 sqr-sin
exp-to-pow associate--r-
neg-sub0
exp-diff associate-+r+ associate--r+ associate--l+
rem-log-exp
associate-+l+ sub-div distribute-neg-frac cos-sum distribute-frac-neg
sqrt-undiv associate--l- asin-acos acos-asin
remove-posit16 cube-unmult exp-neg cos-diff
associate-+r- sqrt-unprod sqrt-pow2 un-div-inv associate-+l- rem-square-sqrt e-exp-1

regimes18.9s

Accuracy

Total 52.5b remaining (37.4%)

12.0b-0.9%Henrywood and Agarwal, Equation (13)
9.8b0%Toniolo and Linder, Equation (13)
7.3b18%Maksimov and Kolovsky, Equation (3)
6.6b46.2%Henrywood and Agarwal, Equation (3)
5.9b75.2%Toniolo and Linder, Equation (7)

localize5.4s

bsearch4.7s

end1.0ms