Details

simplify3.9m (32.1%)

sample3.3m (27.5%)

Algorithm
61×intervals
Results
44.0s253081×body80valid
39.5s28927×body1280valid
27.5s159995×body80nan
20.2s20624×body640valid
17.1s8837×body2560valid
10.5s3428×body5120valid
6.6s9932×body320valid
3.2s8933×body160valid
891.0ms710×body10240exit
444.0ms585×body1280nan
385.0ms630×body640nan
248.0ms8256×pre80true
194.0ms348×body320nan
79.0ms184×body160nan

series2.3m (19.3%)

Calls

435 calls:

7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.6s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

prune1.5m (12.2%)

rewrite41.9s (5.8%)

Algorithm
115×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 (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.4s
(* (* (* (/ (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))
1.3s
(* (* (* (* (/ (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 (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
35545×add-exp-log
24659×prod-exp
12508×pow-exp
10444×div-exp
6868×times-frac
5698×pow-to-exp
5275×add-sqr-sqrt
5007×*-un-lft-identity
4288×add-cube-cbrt
2715×add-cbrt-cube
2078×sqrt-prod
1650×unpow-prod-down
1399×1-exp rec-exp
1301×pow1
1193×cbrt-unprod
1076×associate-*r*
881×associate-*l*
538×add-log-exp
522×cbrt-undiv
505×sqr-pow
484×sqrt-div
438×pow-prod-down
432×associate-/r*
423×associate-*r/
401×cbrt-prod
382×pow-unpow
350×unswap-sqr
343×associate-/l*
335×associate-*l/
326×div-inv
252×frac-times
229×exp-prod
221×distribute-lft-out--
217×associate-/r/
210×distribute-lft-out
192×flip-+ flip3-+
173×sqrt-pow1
172×flip3-- flip--
156×*-commutative
137×difference-of-squares
120×unpow2
111×tan-quot
109×pow1/2
108×distribute-rgt-neg-in
91×clear-num frac-2neg
84×distribute-rgt-in distribute-lft-in
83×distribute-lft-neg-in
81×sub-neg
67×rem-sqrt-square
53×pow-pow
44×frac-sub
42×swap-sqr
40×cbrt-div
39×div-sub
36×pow1/3
34×cube-prod
33×associate-/l/
30×associate--l+
28×sum-log
27×pow-prod-up
25×diff-log
22×frac-add +-commutative
19×cube-div
18×associate--r+
17×pow-sqr
16×cos-sum pow-sub
11×exp-diff neg-mul-1
10×neg-sub0
unpow3 cos-diff cube-mult
un-div-inv rem-exp-log associate-+r+ log-prod
rem-cube-cbrt associate-+l+
pow2 log-pow
pow-plus pow-neg associate--l- sqrt-unprod inv-pow pow-flip acos-asin neg-log exp-sum
rem-square-sqrt distribute-frac-neg rem-cbrt-cube
associate-+r- exp-neg unsub-neg asin-acos associate--r- distribute-neg-frac log-div
sqrt-undiv sqrt-pow2 mul0 rem-log-exp

regimes15.8s (2.2%)

Accuracy

Total 44.7b remaining (20.2%)

Threshold costs 4.1b (1.9%)

8.9b9.2%Toniolo and Linder, Equation (13)
7.2b-17.7%Toniolo and Linder, Equation (10+)
7.2b46.3%Henrywood and Agarwal, Equation (3)
5.4b0%Henrywood and Agarwal, Equation (12)
5.3b77.5%Toniolo and Linder, Equation (7)

localize4.4s (0.6%)

bsearch1.9s (0.3%)

end0.0ms (0.0%)