Details

prune9.7m (42.7%)

simplify7.4m (32.4%)

sample3.0m (13.2%)

Algorithm
61×intervals
Results
44.1s252736×body80valid
37.5s29428×body1280valid
28.1s159195×body80nan
18.2s20197×body640valid
13.8s8725×body2560valid
9.9s3555×body5120valid
6.9s9981×body320valid
4.2s9165×body160valid
964.0ms623×body10240exit
556.0ms644×body1280nan
356.0ms637×body640nan
278.0ms8256×pre80true
105.0ms321×body320nan
41.0ms197×body160nan

series1.5m (6.4%)

Calls

460 calls:

2.4s
(sqrt (* 2 (* (* (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))) (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))) (* (cbrt U) (cbrt (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))))
2.2s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (/ (/ (* (/ M (/ (* d 2) D)) (/ M (/ (* d 2) D))) 2) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
2.1s
(sqrt (* 2 (* (* (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))) (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U)))))))))) (cbrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))))
2.1s
(sqrt (* 2 (* (sqrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))) (sqrt (* U (* n (- t (* (/ l Om) (- (* 2 l) (* (/ l Om) (* n (- U* U))))))))))))
2.0s
(* (* (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))

rewrite43.0s (3.1%)

Algorithm
118×rewrite-expression-head
Calls

460 calls:

13.4s
(sqrt (- 1 (/ (/ (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l))) (/ (/ d (/ (* M D) 2)) (/ (cbrt h) (cbrt l)))) (/ d (/ (* M D) 2)))))
1.1s
(sqrt (- 1 (/ (/ (/ h l) (/ d (/ (* M D) 2))) (/ d (/ (* M D) 2)))))
897.0ms
(/ (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1) NdChar)
575.0ms
(/ 1 (/ (+ (exp (/ (- EDonor (- Ec (+ Vef mu))) KbT)) 1) NdChar))
474.0ms
(* (* (* (* -2 J) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cos (/ K 2)))) (sqrt (+ 1 (pow (/ U (* (* 2 J) (cos (/ K 2)))) 2))))
Rules
197549×times-frac
77073×add-sqr-sqrt
76112×*-un-lft-identity
75225×add-cube-cbrt
30811×cbrt-prod
10851×sqrt-prod
9769×add-exp-log
9329×div-inv
5467×add-cbrt-cube
5012×div-exp
4651×associate-/l*
2890×prod-exp
2765×cbrt-undiv
2004×associate-*l*
1865×unpow-prod-down
1805×associate-/r*
1706×cbrt-unprod
1593×pow1
1434×associate-/r/
1009×associate-*r*
902×associate-*r/
661×sqr-pow
555×sqrt-div
554×add-log-exp
541×frac-times
494×pow-prod-down
460×insert-posit16
456×1-exp
397×associate-*l/
347×distribute-lft-out
343×unswap-sqr
274×flip-+ flip3-+
245×difference-of-squares
226×flip3-- flip--
221×pow-exp
214×rec-exp
204×distribute-rgt-neg-in distribute-lft-neg-in
181×swap-sqr
180×sqrt-pow1
156×cbrt-div *-commutative
124×pow-unpow pow1/2
118×sub-neg
112×unpow-prod-up
109×frac-2neg clear-num
92×tan-quot
88×distribute-lft-out--
87×pow-to-exp
85×associate-/l/
83×pow-prod-up
72×rem-sqrt-square
69×distribute-rgt-in distribute-lft-in
68×neg-mul-1
55×frac-add
47×pow-plus
45×pow-sqr
43×pow1/3
41×distribute-rgt-out
40×sin-mult
34×pow-pow
28×sum-log
26×pow2
23×+-commutative
21×log-pow diff-log
19×exp-prod
17×distribute-lft1-in div-sub
16×pow-flip cos-sum
15×log-prod
12×exp-sum count-2 distribute-rgt1-in
10×cube-prod associate--l+ inv-pow cos-diff
pow3 pow-sub
associate-+l+
unpow2 cube-div
difference-of-sqr--1 difference-of-sqr-1 rem-log-exp acos-asin
associate--r+
exp-diff sqrt-unprod rem-exp-log associate-+l- rem-square-sqrt
remove-posit16 associate-+r- frac-sub sqr-sin un-div-inv distribute-neg-frac asin-acos
neg-sub0 distribute-rgt-out-- unpow3 associate--l- sub-div sqrt-pow2 rem-cbrt-cube cube-mult log-div

regimes20.2s (1.5%)

Accuracy

Total 41.8b remaining (22.9%)

Threshold costs 3.3b (1.8%)

8.4b43.7%Henrywood and Agarwal, Equation (3)
6.8b18.2%Henrywood and Agarwal, Equation (13)
6.2b74.3%Toniolo and Linder, Equation (7)
5.1b45.2%Toniolo and Linder, Equation (13)
4.2b22.4%Henrywood and Agarwal, Equation (12)

localize6.9s (0.5%)

bsearch2.7s (0.2%)

end1.0ms (0.0%)