Details

simplify6.6m (43.7%)

sample3.2m (20.9%)

Algorithm
61×intervals
Results
43.0s253680×body80valid
36.2s29202×body1280valid
26.1s160143×body80nan
20.9s20532×body640valid
19.6s9016×body2560valid
11.4s3411×body5120valid
7.1s9904×body320valid
3.1s8844×body160valid
1.4s652×body10240exit
425.0ms661×body1280nan
343.0ms598×body640nan
152.0ms348×body320nan
132.0ms8256×pre80true
37.0ms202×body160nan

series2.4m (15.5%)

Calls

422 calls:

7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.3s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.9m (12.5%)

rewrite31.2s (3.4%)

Algorithm
113×rewrite-expression-head
Calls

422 calls:

4.6s
(* (sqrt (+ (pow (/ U (* (* (cos (/ K 2.0)) J) 2.0)) 2.0) 1.0)) (* (* (* (cbrt (cos (/ K 2.0))) (* (* (cbrt (cbrt (cos (/ K 2.0)))) (cbrt (cbrt (cos (/ K 2.0))))) (cbrt (cbrt (cos (/ K 2.0)))))) (* (cbrt (cos (/ K 2.0))) J)) -2.0))
1.1s
(* (* (* (* (/ (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))
896.0ms
(* (sqrt (exp (/ (- (+ Vef Ev) (- mu EAccept)) KbT))) (sqrt (exp (/ (- (+ Vef Ev) (- mu EAccept)) KbT))))
772.0ms
(* (* (sqrt (* (- 1.0 (* 3.0 (* v v))) 2.0)) (- (* (* 1.0 1.0) 1.0) (* (* (* v v) (* v v)) (* v v)))) t)
761.0ms
(/ (/ (- 1.0 (* 5.0 (* v v))) PI) (* (* (sqrt (* (- 1.0 (* 3.0 (* v v))) 2.0)) (- (* (* 1.0 1.0) 1.0) (* (* (* v v) (* v v)) (* v v)))) t))
Rules
27815×add-exp-log
18318×prod-exp
8349×pow-exp
8157×div-exp
8024×times-frac
6420×*-un-lft-identity
5918×add-sqr-sqrt
4748×add-cube-cbrt
4185×sqrt-prod
3093×pow-to-exp
2688×add-cbrt-cube
1446×pow1
1027×cbrt-unprod
985×associate-*r*
967×1-exp rec-exp
916×cbrt-prod
854×associate-*l*
739×sqrt-pow1
673×distribute-lft-out--
661×cbrt-undiv
655×associate-/r*
632×exp-prod
619×unpow-prod-down
544×associate-*r/
532×pow-prod-down
513×add-log-exp
470×sqrt-div
334×unswap-sqr
324×distribute-lft-out
317×associate-/l*
305×div-inv
269×associate-*l/
258×flip-+ flip3-+
249×pow-unpow
222×pow-prod-up
214×frac-times
186×associate-/r/
184×sqr-pow
170×pow-sqr
169×flip3-- flip--
136×pow1/3
131×*-commutative
117×swap-sqr
115×difference-of-squares
95×pow1/2
91×frac-add
81×frac-2neg clear-num
77×frac-sub
69×cbrt-div
67×distribute-rgt-in distribute-lft-in
66×rem-sqrt-square
63×pow-plus
58×sub-neg
48×associate-/l/
42×tan-quot pow2
38×pow-pow
35×distribute-lft-neg-in distribute-rgt-neg-in
30×pow3
29×sum-log +-commutative div-sub
18×associate--l+
16×pow-sub diff-log
13×sub-div difference-cubes
12×cos-sum
10×neg-sub0 associate-+r+ pow-neg
associate-+l+ cos-diff
exp-diff
neg-mul-1
pow-flip associate-+r- distribute-rgt-out-- inv-pow associate--r+
cos-mult sqrt-unprod rem-square-sqrt acos-asin distribute-rgt-out
asin-acos distribute-frac-neg rem-cbrt-cube
distribute-lft1-in sqrt-undiv sin-mult count-2 un-div-inv rem-exp-log sqr-cos distribute-rgt1-in

regimes25.9s (2.8%)

Accuracy

Total 56.8b remaining (24.4%)

Threshold costs 5.0b (2.2%)

9.3b4.1%Maksimov and Kolovsky, Equation (3)
9.2b12.6%Toniolo and Linder, Equation (13)
8.4b42.1%Henrywood and Agarwal, Equation (3)
6.7b0%Henrywood and Agarwal, Equation (12)
5.2b77.7%Toniolo and Linder, Equation (7)

localize7.8s (0.9%)

bsearch2.8s (0.3%)

end1.0ms (0.0%)