Details

series1.9m (36.6%)

Calls

441 calls:

6.0s
(log (/ (fma (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 1.0)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* (cbrt (* n (pow (/ l Om) 2.0))) (cbrt (* n (pow (/ l Om) 2.0)))) (cbrt (* n (pow (/ l Om) 2.0)))) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
5.0s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

sample1.4m (26.9%)

Algorithm
61×intervals
Results
15.5s29584×body1280valid
15.4s254654×body80valid
9.8s161103×body80nan
8.7s8804×body2560valid
7.0s20531×body640valid
5.4s3356×body5120valid
2.5s9809×body320valid
1.2s8729×body160valid
443.0ms838×body10240exit
136.0ms597×body1280nan
109.0ms8256×pre80true
105.0ms595×body640nan
52.0ms349×body320nan
15.0ms172×body160nan

prune56.1s (17.7%)

rewrite31.5s (10.0%)

Algorithm
117×rewrite-expression-head
Calls

441 calls:

1.9s
(* (* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.3s
(/ (/ 1 (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ 1 NdChar))
1.1s
(/ (- 1.0 (* 5.0 (* v v))) (* (* PI (* (* t (* (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))) (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))) (cbrt (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3))))))) (- 1.0 (* v v))))
1.0s
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
924.0ms
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
30681×add-exp-log
21326×prod-exp
10445×pow-exp
8665×div-exp
4952×pow-to-exp
4375×times-frac
4292×add-sqr-sqrt
4253×*-un-lft-identity
3313×add-cube-cbrt
2384×add-cbrt-cube
1277×pow1
1009×associate-*r/
991×cbrt-unprod
939×pow-unpow
849×associate-*r*
843×1-exp
841×rec-exp
764×sqrt-prod
662×associate-*l*
612×unpow-prod-down
553×sqrt-div
508×add-log-exp
493×cbrt-prod
482×frac-times
441×log1p-expm1-u expm1-log1p-u
418×pow-prod-down
410×cbrt-undiv
395×distribute-lft-out
377×associate-*l/
341×cbrt-div
333×flip3-- flip--
327×associate-/r*
297×div-inv
292×associate-/l*
273×prod-diff
248×unswap-sqr
204×associate-/r/
200×difference-of-squares
195×sqr-pow
193×flip-+ flip3-+
157×distribute-rgt-in distribute-lft-in
142×*-commutative
139×distribute-lft-out-- sqrt-pow1
127×distribute-rgt-neg-in
109×exp-prod
94×fma-def
91×pow1/3
90×clear-num frac-2neg
79×pow1/2
73×swap-sqr
72×tan-quot
62×distribute-lft-neg-in
61×pow-pow
53×rem-sqrt-square
46×sub-neg
45×frac-sub
44×div-sub
43×log-prod
41×associate-/l/
34×pow-prod-up
32×associate--l+
26×fma-udef pow-sqr
25×unpow2 cube-prod sum-log
23×cos-sum
20×exp-sum
19×fma-neg +-commutative
16×exp-neg distribute-rgt-neg-out
14×pow-sub hypot-def
13×neg-sub0
12×log-pow
11×frac-add
10×exp-diff un-div-inv pow2
9×pow-plus
8×mul-1-neg log-rec
7×diff-log inv-pow pow-flip neg-mul-1
6×rem-exp-log associate-+r- unsub-neg
5×unpow3 cube-mult
4×cube-div sub-div acos-asin pow-neg rem-log-exp
3×neg-log distribute-neg-frac associate-+l-
2×rem-cube-cbrt sqrt-pow2 associate-+l+ associate-+r+ sqrt-unprod hypot-udef expm1-log1p rem-square-sqrt asin-acos expm1-udef log-div
1×sqrt-undiv cos-diff mul0 distribute-rgt-out-- rem-cbrt-cube

simplify11.4s (3.6%)

regimes10.3s (3.3%)

Accuracy

Total 38.8b remaining (21.1%)

Threshold costs 5.7b (3.1%)

7.8b14.3%Toniolo and Linder, Equation (13)
6.8b12.7%Toniolo and Linder, Equation (10+)
5.2b-19.9%Henrywood and Agarwal, Equation (12)
5.1b78.3%Toniolo and Linder, Equation (7)
3.3b51%Toniolo and Linder, Equation (10-)

bsearch3.6s (1.1%)

localize2.3s (0.7%)

end1.0ms (0.0%)