Details

prune14.4m (53.7%)

simplify5.8m (21.7%)

sample4.3m (16.0%)

Algorithm
60×intervals
Results
1.0m256856×body80valid
48.8s27623×body1280valid
41.7s159692×body80nan
24.5s18900×body640valid
19.9s8502×body10240exit
14.8s8045×body2560valid
10.7s3381×body5120valid
9.5s9559×body320valid
4.8s9215×body160valid
672.0ms597×body1280nan
583.0ms664×body640nan
308.0ms8256×pre80true
168.0ms320×body320nan
73.0ms219×body160nan

series1.3m (4.7%)

Calls

443 calls:

Slowest
4.7s
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))
4.3s
(sqrt (+ (* (/ (* -2 n) (/ (/ Om l) l)) (* U 2)) (* (* U 2) (* n (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))))
2.0s
(sqrt (* U (* 2 (* n (+ (/ -2 (/ Om (* l l))) (- t (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))))
1.6s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.5s
(sqrt (+ (* (/ -2 (/ 1 (* (cbrt l) (cbrt l)))) (* (/ n (/ (/ Om l) (cbrt l))) (* U 2))) (* (* U 2) (* n (- t (* (/ (/ 1 (/ 1 (* (cbrt l) (cbrt l)))) Om) (* (/ (/ n (/ Om (cbrt l))) (/ 1 l)) (- U U*))))))))

rewrite35.3s (2.2%)

Algorithm
114×rewrite-expression-head
Calls

443 calls:

Slowest
4.2s
(* (+ (/ (/ (/ (/ c0 w) (/ D d)) (/ D d)) h) (sqrt (- (* (/ (/ (/ (/ c0 w) (/ D d)) (/ D d)) h) (/ (/ (/ (/ c0 w) (/ D d)) (/ D d)) h)) (* M M)))) (/ c0 w))
1.3s
(/ (/ (/ NaChar (sqrt (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT)))))) (sqrt (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT)))))) (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT)))))
1.1s
(+ (/ (/ (/ (/ c0 w) (/ D d)) (/ D d)) h) (sqrt (- (* (/ (/ (/ (/ c0 w) (/ D d)) (/ D d)) h) (/ (/ (/ (/ c0 w) (/ D d)) (/ D d)) h)) (* M M))))
922.0ms
(cbrt (* (* (* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* (* l 1/3) l))))) (cos (/ K 2))) (* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* (* l 1/3) l))))) (cos (/ K 2)))) (* (* J (+ (* (pow l 5) 1/60) (* l (+ 2 (* (* l 1/3) l))))) (cos (/ K 2)))))
906.0ms
(/ (/ NaChar (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT))))) (sqrt (+ 1 (exp (/ (- (+ (+ EAccept Vef) Ev) mu) KbT)))))
Rules
99735×times-frac
46826×sqrt-prod
45929×*-un-lft-identity
44653×add-sqr-sqrt
43279×add-cube-cbrt
8891×associate-*l*
8487×add-exp-log
7892×add-cbrt-cube
3729×div-exp
3487×cbrt-undiv
3464×div-inv
2785×associate-/l*
2778×prod-exp
2587×cbrt-unprod
1376×pow1
1348×sqrt-div
1130×associate-*r/
1129×distribute-lft-out
1044×associate-/r/
1004×cbrt-prod
797×associate-/r*
679×associate-*r*
631×frac-times
515×add-log-exp
506×associate-*l/
479×cbrt-div
443×insert-posit16
409×flip-+ flip3-+
400×flip3-- flip--
397×pow-prod-down
354×unswap-sqr
205×difference-of-squares
189×distribute-lft-out--
157×sqrt-pow1
151×*-commutative
136×unpow-prod-down
129×pow-unpow swap-sqr
126×frac-2neg clear-num
124×pow1/2
103×associate-/l/
102×sqr-pow
93×rem-sqrt-square
88×frac-add
82×pow-exp
78×distribute-rgt-in distribute-lft-in
64×sin-mult
62×1-exp rec-exp
61×pow-prod-up
52×sub-neg
48×pow-to-exp
41×pow-plus
40×pow1/3
35×frac-sub
33×div-sub
31×tan-quot
29×pow-sqr
27×distribute-rgt-out--
23×pow2 pow-pow
19×diff-log
18×sum-log
17×pow-sub
16×associate--l+
15×+-commutative
13×pow-flip
10×inv-pow cos-sum cube-prod
8×associate--r+ sqr-sin log-pow
7×un-div-inv
6×log-prod cube-unmult cube-div
4×associate-+r+ pow3 difference-of-sqr-1 exp-to-pow
3×associate--l- asin-acos rem-cbrt-cube acos-asin
2×associate-+l+ remove-posit16 sqrt-unprod sqrt-pow2 rem-square-sqrt cos-diff exp-prod rem-log-exp
1×associate-+r- sqrt-undiv unpow3 sub-div cube-mult distribute-rgt-out

regimes18.5s (1.2%)

Accuracy

Total 48.4b remaining (25.6%)

Threshold costs 5.4b (2.9%)

8.7b-2%Maksimov and Kolovsky, Equation (3)
7.8b18.2%Henrywood and Agarwal, Equation (13)
7.6b44.5%Henrywood and Agarwal, Equation (3)
5.5b37.8%Toniolo and Linder, Equation (13)
5.1b78.3%Toniolo and Linder, Equation (7)

localize6.5s (0.4%)

bsearch1.9s (0.1%)

end1.0ms (0.0%)