Details

simplify6.2m (41.6%)

sample3.5m (23.2%)

Algorithm
61×intervals
Results
45.2s253418×body80valid
41.1s29403×body1280valid
29.2s160338×body80nan
18.7s20091×body640valid
18.5s8792×body2560valid
12.3s3435×body5120valid
7.4s10024×body320valid
3.7s8958×body160valid
819.0ms669×body10240exit
448.0ms591×body1280nan
328.0ms8256×pre80true
265.0ms610×body640nan
107.0ms352×body320nan
37.0ms188×body160nan

series2.5m (16.9%)

Calls

449 calls:

7.7s
(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*)))))
7.6s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))
7.4s
(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*)))))
2.1s
(* (* (* 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*))))

prune1.5m (10.1%)

rewrite48.8s (5.5%)

Algorithm
118×rewrite-expression-head
Calls

449 calls:

1.6s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.6s
(- (- (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 t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
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))
Rules
56104×add-exp-log
41507×prod-exp
28823×pow-exp
19737×div-exp
12802×pow-to-exp
9169×times-frac
7172×add-sqr-sqrt
5918×*-un-lft-identity
4986×add-cube-cbrt
4794×1-exp
4788×rec-exp
2660×sqrt-prod
2487×add-cbrt-cube
1923×unpow-prod-down
1581×associate-*l*
1311×pow1
1020×cbrt-unprod
1000×associate-*r*
806×sqr-pow
750×difference-of-squares
558×add-log-exp
504×pow-unpow
458×cbrt-undiv
456×associate-/l*
443×associate-*r/
432×associate-/r*
424×unswap-sqr
416×div-inv
409×cbrt-prod
402×pow-prod-down
352×associate-*l/
318×sqrt-div
274×frac-times
267×distribute-lft-out--
243×distribute-lft-out
224×exp-prod
217×flip-+ flip3-+
191×flip3-- flip--
163×associate-/r/
154×cube-prod
147×*-commutative
143×cbrt-div
112×sqrt-pow1
111×unpow2
107×tan-quot
88×cube-div frac-2neg clear-num
77×distribute-rgt-in distribute-lft-in
75×pow1/2
69×pow1/3
64×rem-sqrt-square
63×sub-neg
62×pow-pow
51×pow-prod-up
43×associate-/l/
36×frac-sub
35×div-sub
33×pow-sqr
32×swap-sqr
31×sum-log
30×distribute-rgt-neg-in
26×distribute-lft-neg-in associate--l+
23×+-commutative
22×diff-log pow-plus
21×rem-cube-cbrt log-prod
17×pow2
16×frac-add log-pow
15×pow-sub
12×unpow3 pow-flip cube-mult
11×rem-exp-log
9×exp-diff inv-pow
8×associate-+r+ neg-sub0 pow-neg associate-+r-
6×cos-sum acos-asin associate--r+
5×exp-sum rem-log-exp
4×neg-log asin-acos
3×distribute-rgt-out-- cos-diff
2×un-div-inv associate--l- associate-+l+ sub-div neg-mul-1 associate--r- rem-cbrt-cube exp-to-pow log-div
1×sqrt-unprod rem-square-sqrt mul0 exp-lft-cube

regimes15.9s (1.8%)

Accuracy

Total 42.8b remaining (20.3%)

Threshold costs 4.8b (2.3%)

9.3b25.7%Toniolo and Linder, Equation (13)
5.9b75.5%Toniolo and Linder, Equation (7)
5.6b4%Henrywood and Agarwal, Equation (12)
4.8b32.8%Toniolo and Linder, Equation (10+)
4.6b-47.3%Henrywood and Agarwal, Equation (13)

localize4.5s (0.5%)

bsearch3.6s (0.4%)

end0.0ms (0.0%)