Details

simplify56.2m

Calls

17410 calls:

Slowest
3.1s
(* (* (/ (* (* (* 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 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)))
2.4s
(* (* (/ (* (* (* 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 l) (/ h l)) (/ h l)))
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)))
2.3s
(* (* (/ (* (* (* 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)))

prune3.7m

sample3.4m

Algorithm
56×intervals
Results
55.0s232496×body80valid
39.8s151353×body80nan
29.7s18831×body1280valid
19.4s8373×body10240exit
16.1s12779×body640valid
9.3s5892×body2560valid
5.9s6699×body320valid
5.5s2443×body5120valid
5.0s7719×body160valid
941.0ms8256×pre80true
696.0ms565×body1280nan
582.0ms616×body640nan
232.0ms385×body320nan
64.0ms200×body160nan

series1.3m

Calls

411 calls:

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

rewrite28.8s

Algorithm
109×rewrite-expression-head
Calls

411 calls:

Slowest
3.1s
(* (sqrt (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)) (sqrt (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)))
810.0ms
(+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)
807.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
730.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
546.0ms
(/ (- (* (+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4)) (+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4))) (* 1 1)) (+ (+ (* (* b b) 4) (pow (sqrt (+ (* a a) (* b b))) 4)) 1))
Rules
92264×times-frac
34829×add-sqr-sqrt
34747×*-un-lft-identity
33797×add-cube-cbrt
19825×sqrt-prod
5610×add-exp-log
4160×add-cbrt-cube
2792×div-inv
2088×associate-/r/
2084×div-exp
2009×prod-exp
1870×cbrt-prod
1827×pow1
1507×cbrt-undiv
1455×cbrt-unprod
1363×associate-/l*
1252×sqrt-div
850×associate-*r*
835×associate-*r/
778×associate-*l*
721×associate-/r*
716×associate-*l/
693×frac-times
690×flip-+ flip3-+
581×pow-prod-down
528×add-log-exp
411×insert-posit16
354×distribute-lft-out
290×unpow-prod-down
285×pow-unpow
251×unswap-sqr
247×pow-prod-up
237×difference-of-squares
235×pow1/3
206×flip3-- flip--
201×pow-exp
192×distribute-lft-out--
190×frac-add
182×swap-sqr
161×pow-sqr
159×sqr-pow
150×*-commutative
136×sqrt-pow1
124×1-exp
118×distribute-rgt-neg-in
115×tan-quot
112×distribute-lft-neg-in
110×pow1/2
101×pow-plus
90×pow-to-exp
88×rec-exp
87×cbrt-div
86×frac-sub
80×sin-mult
74×pow2
72×rem-sqrt-square
69×frac-2neg clear-num
66×sub-neg
62×distribute-rgt-in distribute-lft-in
53×associate-/l/
39×diff-log
30×pow-pow
24×sum-log
23×div-sub
21×+-commutative
20×associate--l+
16×neg-mul-1
14×log-pow
13×exp-prod
10×pow-flip associate--r+ cube-prod
pow-sub
inv-pow distribute-neg-frac
neg-sub0 unpow2
log-prod neg-log cube-div
associate--r-
associate-+r+ distribute-frac-neg sqr-sin distribute-rgt-out-- unpow1/3
cube-unmult associate--l- exp-to-pow asin-acos
associate-+l+ remove-posit16 associate-+r- pow3 difference-of-sqr-1 sqrt-unprod rem-log-exp rem-square-sqrt cos-sum acos-asin
sqrt-undiv unpow3 sub-div sqrt-pow2 rem-exp-log cube-mult cos-diff rem-cbrt-cube

regimes16.3s

Accuracy

Total 67.2b remaining (36.2%)

Threshold costs 3.5b (1.9%)

13.2b-7%Maksimov and Kolovsky, Equation (32)
12.8b-11.2%Henrywood and Agarwal, Equation (13)
8.8b16.1%Toniolo and Linder, Equation (13)
8.1b9.5%Maksimov and Kolovsky, Equation (3)
7.9b47.2%Henrywood and Agarwal, Equation (3)

bsearch7.1s

localize6.3s

end1.0ms