Details

simplify5.6m (39.5%)

sample3.4m (23.6%)

Algorithm
61×intervals
Results
49.0s252717×body80valid
41.1s29655×body1280valid
29.1s160168×body80nan
19.6s8784×body2560valid
18.1s19798×body640valid
12.2s3453×body5120valid
6.6s10182×body320valid
3.0s9191×body160valid
1.2s635×body10240exit
452.0ms596×body1280nan
449.0ms8256×pre80true
353.0ms621×body640nan
164.0ms362×body320nan
39.0ms209×body160nan

series2.5m (17.8%)

Calls

432 calls:

7.8s
(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*)))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.4s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

prune1.5m (10.6%)

rewrite48.5s (5.7%)

Algorithm
113×rewrite-expression-head
Calls

432 calls:

2.6s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
2.6s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
1.9s
(* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.6s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
Rules
47328×add-exp-log
33318×prod-exp
21400×pow-exp
16320×div-exp
13729×times-frac
11779×sqrt-prod
11098×add-sqr-sqrt
10301×pow-to-exp
9607×*-un-lft-identity
5919×add-cube-cbrt
2371×add-cbrt-cube
2199×unpow-prod-down
2124×difference-of-squares
1929×1-exp rec-exp
1365×associate-*l*
1314×distribute-lft-out
1227×pow1
958×associate-*r*
904×cbrt-unprod
747×sqr-pow
562×add-log-exp
559×cbrt-prod
522×distribute-lft-out--
458×associate-*r/
439×cbrt-undiv
438×sqrt-div
372×unswap-sqr
365×pow-unpow
356×pow-prod-down
325×div-inv
319×associate-/l*
313×associate-/r*
276×associate-/r/
271×associate-*l/
239×frac-times
217×flip-+ flip3-+
203×flip-- flip3--
143×*-commutative
130×sqrt-pow1
100×tan-quot
91×rem-sqrt-square
89×pow1/2 frac-2neg clear-num
80×exp-prod
72×distribute-rgt-in distribute-lft-in
67×sub-neg
57×associate-/l/ unpow2
47×pow-prod-up
45×pow-pow
42×cube-prod frac-sub
41×pow1/3
39×distribute-rgt-neg-in
36×diff-log
33×div-sub sum-log
30×associate--l+
29×pow-sqr
27×pow-sub
26×distribute-lft-neg-in
25×+-commutative
24×frac-add
22×swap-sqr
20×pow-plus
18×cbrt-div
15×log-pow pow2
14×neg-log associate--r+
13×rem-exp-log neg-sub0
12×log-prod
exp-sum
cos-sum inv-pow pow-flip associate-+r+ pow-neg
associate--r-
unpow3 un-div-inv cube-mult acos-asin
cube-div exp-diff cos-diff distribute-neg-frac associate-+l-
associate--l- unpow-prod-up
rem-cube-cbrt associate-+l+ associate-+r- asin-acos neg-mul-1 rem-cbrt-cube
e-exp-1 quot-tan sqrt-unprod rem-square-sqrt mul0 rem-log-exp

regimes15.7s (1.8%)

Accuracy

Total 43.1b remaining (19.9%)

Threshold costs 3.8b (1.8%)

8.8b19.3%Toniolo and Linder, Equation (13)
6.7b-20%Maksimov and Kolovsky, Equation (3)
5.7b76.5%Toniolo and Linder, Equation (7)
4.6b15.2%Toniolo and Linder, Equation (10+)
3.7b34.5%Toniolo and Linder, Equation (10-)

bsearch4.5s (0.5%)

localize4.3s (0.5%)

end0.0ms (0.0%)