Details

simplify32.9m

Calls

12206 calls:

Slowest
3.3s
(* (* (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* (* M M) M) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))) (* (* (/ (cbrt h) (cbrt l)) (/ (cbrt h) (cbrt l))) (/ (cbrt h) (cbrt l))))
2.8s
(* (* (/ (* (* (* 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) (* l l)))
2.8s
(* (* (/ (* (* (* 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)))
2.6s
(* (* (/ (* (* (* 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)))
2.6s
(* (* (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (* (* (/ D d) (/ D d)) (/ D d)))) (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (/ (* (* 2 2) 2) (/ (* (* D D) D) (* (* d d) d))))) (/ h l))

prune3.8m

sample3.5m

Algorithm
54×intervals
Results
58.3s239242×body80valid
42.2s158766×body80nan
34.0s18116×body1280valid
19.7s8655×body10240exit
17.0s14018×body640valid
7.2s4963×body2560valid
6.4s7012×body320valid
5.0s2348×body5120valid
4.1s8102×body160valid
696.0ms637×body1280nan
467.0ms623×body640nan
172.0ms343×body320nan
93.0ms195×body160nan

series1.2m

Calls

410 calls:

Slowest
1.8s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l))))
1.7s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (cbrt d)) (pow (/ (cbrt d) l) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.7s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))

rewrite30.0s

Algorithm
104×rewrite-expression-head
Calls

410 calls:

Slowest
6.7s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1)) -2) (cos (/ K 2))) J)
1.3s
(* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J)
917.0ms
(+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)
822.0ms
(sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (* (cos (/ K 2)) (* (cbrt J) (cbrt J))) (cbrt J))))) 1))
333.0ms
(/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)
Rules
89100×times-frac
32714×add-sqr-sqrt
32514×*-un-lft-identity
31875×add-cube-cbrt
9605×add-exp-log
6618×add-cbrt-cube
5167×div-inv
3927×prod-exp
3717×div-exp
3057×associate-/r/
2968×cbrt-undiv
2669×cbrt-unprod
1833×pow1
1270×flip-+ flip3-+
930×associate-/l*
884×associate-*l*
744×associate-*r*
680×sqrt-prod
640×associate-/r*
555×associate-*r/
513×pow-prod-down
486×add-log-exp
449×frac-times
447×associate-*l/
434×sqrt-div
410×insert-posit16
369×pow-exp
304×pow-unpow
236×unswap-sqr
216×pow-prod-up
196×flip3-- flip--
189×cbrt-prod difference-of-squares
182×distribute-lft-out--
173×*-commutative
170×1-exp
163×distribute-lft-out
149×swap-sqr
141×unpow-prod-down
138×frac-add
128×sqrt-pow1
127×rec-exp
125×pow-to-exp
121×pow-sqr
117×tan-quot
112×distribute-lft-neg-in distribute-rgt-neg-in
107×pow-plus
94×pow1/2
83×frac-2neg clear-num
79×pow2
68×distribute-rgt-in distribute-lft-in
58×sub-neg rem-sqrt-square
56×sin-mult
51×sqr-pow
50×cbrt-div
47×associate-/l/
44×log-prod
36×frac-sub
35×pow1/3
34×associate-+l+
32×pow-pow exp-prod
26×div-sub
23×sum-log log-pow
21×+-commutative
17×diff-log
16×neg-mul-1
14×associate-+r+
11×pow-flip
10×sqr-sin log-div
inv-pow pow-sub
distribute-rgt-out-- distribute-neg-frac
associate--l+
associate-+r-
remove-posit16 pow3 difference-of-sqr-1 rem-log-exp
neg-sub0 distribute-frac-neg associate--r+ cos-sum acos-asin
exp-diff
distribute-lft1-in cos-mult cube-unmult un-div-inv unpow2 asin-acos rem-exp-log cos-diff associate--r- distribute-rgt-out
exp-sum unpow1/2 sqrt-unprod sub-div sqrt-pow2 exp-to-pow associate-+l- rem-square-sqrt

regimes16.6s

Accuracy

Total 50.4b remaining (31.5%)

9.1b-12%Toniolo and Linder, Equation (13)
8.0b8.1%Henrywood and Agarwal, Equation (13)
7.7b7.7%Maksimov and Kolovsky, Equation (3)
6.6b1.2%Henrywood and Agarwal, Equation (12)
6.4b73.1%Toniolo and Linder, Equation (7)

localize6.0s

bsearch4.9s

end1.0ms