Details

simplify54.9m

Calls

19507 calls:

Slowest
3.1s
(* (* (/ (* (* (* 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))))
3.0s
(* (* (/ (* (* (* 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) (* l l)))
2.9s
(* (* (/ (* (* (* 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)))
2.9s
(* (* (/ (* (* (* 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) (* l l)))
2.9s
(* (* (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d)))) (/ (* (* (* M (/ (cbrt h) (cbrt l))) (* M (/ (cbrt h) (cbrt l)))) (* M (/ (cbrt h) (cbrt l)))) (* (* (/ 2 (/ D d)) (/ 2 (/ D d))) (/ 2 (/ D d))))) (/ h l))

prune5.4m

sample3.9m

Algorithm
59×intervals
Results
1.1m255822×body80valid
42.8s161168×body80nan
39.8s23647×body1280valid
22.8s16721×body640valid
20.1s8666×body10240exit
8.1s5764×body2560valid
7.8s8619×body320valid
5.3s2467×body5120valid
4.9s8688×body160valid
653.0ms646×body1280nan
626.0ms641×body640nan
511.0ms190×body160nan
311.0ms8256×pre80true
190.0ms333×body320nan

series1.4m

Calls

439 calls:

Slowest
2.4s
(sqrt (* 2 (+ (* (* U n) t) (* (/ U (/ Om (* n l))) (- (* -2 l) (/ (- U U*) (/ Om (* n 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))))))))
1.6s
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))
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) (/ 1 l))))

rewrite40.0s

Algorithm
113×rewrite-expression-head
Calls

439 calls:

Slowest
6.6s
(* (cbrt (/ NdChar (+ (* (* (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) 1))) (cbrt (/ NdChar (+ (* (* (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) 1))))
1.5s
(/ NdChar (+ (* (* (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) (cbrt (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)))) 1))
1.4s
(/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1))
1.2s
(* (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))) (+ 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))))
1.0s
(/ (- (* 1 1) (* (* 5 (* v v)) (* 5 (* v v)))) (* (* (* PI (* t (sqrt (* 2 (- 1 (* 3 (* v v))))))) (- (pow 1 3) (pow (* v v) 3))) (+ 1 (* 5 (* v v)))))
Rules
14576×times-frac
9685×add-exp-log
8275×add-sqr-sqrt
8029×*-un-lft-identity
7190×add-cube-cbrt
6423×add-cbrt-cube
4125×prod-exp
3832×sqrt-prod
3525×div-exp
2756×cbrt-undiv
2689×cbrt-unprod
2148×frac-times
1478×pow1
1456×associate-*r/
1196×associate-/l*
1178×sqrt-div
1147×flip3-- flip--
983×associate-*r*
838×associate-*l*
830×associate-*l/
784×associate-/r/
714×div-inv
679×cbrt-prod
609×associate-/r*
580×cbrt-div
550×add-log-exp
457×pow-prod-down
445×flip-+ flip3-+
439×insert-posit16
420×pow-exp
280×exp-sum
269×unswap-sqr
263×difference-of-squares
254×distribute-lft-out
235×unpow-prod-down
232×distribute-rgt-in distribute-lft-in frac-add
211×distribute-lft-out--
194×pow-unpow
174×1-exp
169×rec-exp
168×*-commutative
163×sqrt-pow1
161×distribute-lft-neg-in distribute-rgt-neg-in
159×pow-to-exp
151×swap-sqr
135×tan-quot
114×sqr-pow
111×pow1/2
101×frac-2neg clear-num
80×pow-prod-up
74×sin-mult
72×sub-neg
69×exp-prod
59×associate-/l/
55×rem-sqrt-square
50×pow1/3
43×pow-plus
35×sum-log
31×cube-prod pow-sqr
30×div-sub
29×pow-flip pow-pow
26×+-commutative
25×pow2
24×diff-log
23×neg-mul-1
15×log-prod
13×frac-sub associate-+r+ associate--l+ difference-of-sqr-1 pow-sub
12×inv-pow un-div-inv
10×distribute-neg-frac
sqr-sin
associate-+l+ neg-sub0 distribute-frac-neg log-div
remove-posit16 distribute-rgt-out-- cube-unmult log-pow
exp-diff associate-+r- pow-div asin-acos cos-sum acos-asin
unpow-prod-up rem-exp-log distribute-rgt-out
distribute-lft1-in rem-cube-cbrt rem-log-exp cos-diff
sqrt-undiv unpow1/2 unpow3 sqrt-unprod sub-div sqrt-pow2 associate--r+ difference-cubes exp-neg unpow2 rem-square-sqrt cube-div cube-mult e-exp-1

regimes20.2s

Accuracy

Total 40.0b remaining (21.1%)

9.8b-9%Toniolo and Linder, Equation (13)
8.2b6.5%Maksimov and Kolovsky, Equation (3)
5.4b77.4%Toniolo and Linder, Equation (7)
3.8b11.5%Henrywood and Agarwal, Equation (13)
3.5b47.3%Henrywood and Agarwal, Equation (12)

localize6.7s

bsearch6.7s

end1.0ms