Details

simplify5.9m (41.9%)

sample3.4m (24.0%)

Algorithm
61×intervals
Results
43.0s253181×body80valid
40.3s29050×body1280valid
30.3s159688×body80nan
19.8s8830×body2560valid
18.5s20399×body640valid
10.5s3436×body5120valid
6.4s9922×body320valid
4.4s9089×body160valid
785.0ms662×body10240exit
421.0ms621×body1280nan
272.0ms627×body640nan
261.0ms8256×pre80true
139.0ms376×body320nan
40.0ms166×body160nan

series2.4m (17.3%)

Calls

435 calls:

8.0s
(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*)))))
7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (* (cbrt (/ l Om)) (cbrt (/ l Om))) 2.0)) (pow (cbrt (/ l Om)) 2.0)) (- U U*)))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.0s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.3m (9.1%)

rewrite40.1s (4.7%)

Algorithm
114×rewrite-expression-head
Calls

435 calls:

2.3s
(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(* (* (* (* (/ (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))
1.3s
(* (/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)))) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.0s
(+ (cbrt (pow (/ (* c0 (* d d)) (* (* w h) (* D D))) 3)) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
933.0ms
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))
Rules
55731×add-exp-log
41287×prod-exp
28838×pow-exp
19741×div-exp
12864×pow-to-exp
4963×times-frac
4803×rec-exp 1-exp
4496×add-sqr-sqrt
4071×*-un-lft-identity
3549×add-cube-cbrt
3253×sqrt-prod
2472×add-cbrt-cube
1463×sqrt-div
1235×pow1
1155×associate-*l*
1144×frac-times
970×cbrt-unprod
856×unpow-prod-down
841×associate-*r*
737×associate-*r/
666×flip-- flip3--
616×associate-*l/
530×add-log-exp
509×cbrt-prod
446×cbrt-undiv
406×pow-prod-down
378×pow-unpow
373×associate-/r*
364×associate-/l*
299×unswap-sqr
281×div-inv
209×sqr-pow
200×associate-/r/
174×distribute-lft-out
159×flip-+ flip3-+
142×*-commutative
140×difference-of-squares
124×sqrt-pow1
111×tan-quot
104×cbrt-div
101×distribute-lft-out--
91×clear-num frac-2neg
86×pow1/3
81×exp-prod
75×log-pow
70×distribute-rgt-in distribute-lft-in
63×sub-neg
58×pow1/2
50×pow-pow
47×unpow2
45×rem-sqrt-square
43×cube-prod
41×swap-sqr
34×frac-sub
33×sum-log
30×associate-/l/ log-prod
25×+-commutative pow-prod-up
21×frac-add
20×associate--l+
19×pow-sqr div-sub
17×diff-log
13×distribute-lft-neg-in associate-+r+ distribute-rgt-neg-in
10×pow-sub
9×exp-sum
8×associate--r+
6×cos-sum inv-pow pow-flip rem-log-exp
5×cube-div exp-diff rem-cube-cbrt pow2 unpow3 cube-mult pow-plus
4×acos-asin pow-neg log-div
3×associate-+l+ associate--l- distribute-rgt-out-- cos-diff unpow-prod-up neg-sub0 asin-acos
2×sqrt-undiv e-exp-1 un-div-inv rem-exp-log associate-+r- rem-cbrt-cube
1×sqrt-unprod rem-square-sqrt distribute-rgt-out sub-div neg-mul-1 mul0 exp-to-pow

regimes17.1s (2.0%)

Accuracy

Total 43.7b remaining (20.3%)

Threshold costs 5.6b (2.6%)

8.8b14.8%Toniolo and Linder, Equation (13)
7.9b-13.1%Henrywood and Agarwal, Equation (12)
7.8b-0.7%Toniolo and Linder, Equation (10+)
5.2b78.1%Toniolo and Linder, Equation (7)
4.8b19.7%Toniolo and Linder, Equation (10-)

bsearch5.0s (0.6%)

localize4.4s (0.5%)

end1.0ms (0.0%)