Details

simplify31.0m

Calls

11179 calls:

Slowest
2.6s
(* (* (/ (* (* (* 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)))
2.6s
(* (* (/ (* (* (* 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)))
2.5s
(* (* (/ (* (* (* 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)))
2.3s
(* (* (* (* (* M M) M) (* (* D D) D)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* h h) h))

prune3.6m

sample3.5m

Algorithm
54×intervals
Results
57.7s239885×body80valid
43.1s160366×body80nan
31.2s18133×body1280valid
19.5s8561×body10240exit
18.3s14196×body640valid
7.1s7159×body320valid
6.4s4827×body2560valid
5.5s2386×body5120valid
4.0s8025×body160valid
691.0ms649×body1280nan
578.0ms651×body640nan
268.0ms361×body320nan
123.0ms190×body160nan

series1.2m

Calls

404 calls:

Slowest
1.7s
(sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))))
1.6s
(* (* (/ (+ EAccept (- (+ Ev Vef) mu)) KbT) (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)) (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))
1.6s
(sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n))))))))
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
1.3s
(sqrt (+ (* t (* (* (* 2 n) U) 1)) (* (* (* (* (/ l Om) n) U) (- (* l -2) (* (* (/ l Om) n) (- U U*)))) 2)))

rewrite27.8s

Algorithm
104×rewrite-expression-head
Calls

404 calls:

Slowest
1.4s
(* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (* (cbrt (cos (/ K 2))) (* (* (cbrt (cbrt (cos (/ K 2)))) (cbrt (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2)))))) (* (cbrt (cos (/ K 2))) J)))
1.2s
(- (* (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)) (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))) (* 1 (exp (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))))
696.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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)) (/ (* (cbrt h) (cbrt h)) (* (cbrt l) (cbrt l)))) (/ (cbrt h) (cbrt l)))))
649.0ms
(* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (pow (/ 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 l))))
631.0ms
(* (* (/ (+ EAccept (- (+ Ev Vef) mu)) KbT) (/ (+ EAccept (- (+ Ev Vef) mu)) KbT)) (/ (+ EAccept (- (+ Ev Vef) mu)) KbT))
Rules
33218×times-frac
15005×*-un-lft-identity
14938×add-sqr-sqrt
14145×add-cube-cbrt
7248×add-exp-log
6100×sqrt-prod
4640×add-cbrt-cube
3280×prod-exp
2240×div-exp
1765×cbrt-unprod
1570×cbrt-undiv
1418×pow1
1267×div-inv
1083×associate-/r/
867×associate-/l*
815×associate-*l*
751×sqrt-div
671×associate-*r*
588×associate-*r/
510×pow-prod-down
505×pow-exp
497×frac-times
486×associate-/r*
451×add-log-exp
429×pow-unpow
422×associate-*l/
404×insert-posit16
374×flip-+ flip3-+
247×distribute-lft-out
221×cbrt-prod
220×unswap-sqr
208×flip3-- flip--
201×pow-to-exp
195×distribute-lft-out--
187×difference-of-squares
184×unpow-prod-down
158×swap-sqr
151×*-commutative
139×sqrt-pow1
121×exp-prod
120×1-exp
114×tan-quot
109×rec-exp
103×pow1/2
92×frac-add
81×frac-2neg clear-num
75×distribute-rgt-in distribute-lft-in
71×cbrt-div
67×div-sub
65×rem-sqrt-square
60×sub-neg
57×sqr-pow
56×pow1/3
51×associate-/l/
50×pow-prod-up
43×sin-mult
41×distribute-rgt-out-- log-pow
35×pow-pow
28×distribute-lft-neg-in distribute-rgt-neg-in
26×pow-plus
25×pow-sub pow-sqr
21×frac-sub
19×log-prod
17×pow2
16×associate-+r-
15×exp-diff
14×sum-log
12×pow-flip +-commutative
un-div-inv
inv-pow
associate-+l+ sub-div diff-log
associate--l+ rem-log-exp unpow2 rem-exp-log cos-sum acos-asin
associate-+r+ neg-mul-1 sum-cubes
exp-sum sqr-sin cos-diff
cube-unmult pow3 sqrt-unprod distribute-neg-frac asin-acos rem-square-sqrt
neg-sub0 sqrt-undiv distribute-frac-neg sqrt-pow2 exp-to-pow rem-cbrt-cube

regimes19.1s

Accuracy

Total 44.8b remaining (28.1%)

8.5b5%Toniolo and Linder, Equation (13)
7.9b8%Maksimov and Kolovsky, Equation (3)
7.7b46%Henrywood and Agarwal, Equation (3)
5.5b76.9%Toniolo and Linder, Equation (7)
4.6b0%Henrywood and Agarwal, Equation (12)

localize6.0s

bsearch2.4s

end2.0ms