Details

simplify6.3m (53.9%)

series2.5m (21.4%)

Calls

449 calls:

7.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.3s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.3s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*))))))
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*)))))
2.1s
(* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (* 2 (/ 2.0 2)))) (- U U*)))))

prune1.6m (13.4%)

rewrite47.1s (6.7%)

Algorithm
118×rewrite-expression-head
Calls

449 calls:

1.5s
(* (* (* (/ (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 (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (/ (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (* (cbrt l) (cbrt l))) (/ h (cbrt l)))))
1.2s
(* (* (* (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))
1.1s
(* (* (* (/ (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))
990.0ms
(+ (/ (* 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
45043×add-exp-log
32460×prod-exp
20159×pow-exp
14503×div-exp
9425×times-frac
9063×pow-to-exp
7330×add-sqr-sqrt
6036×*-un-lft-identity
5124×add-cube-cbrt
2740×sqrt-prod
2712×1-exp rec-exp
2502×add-cbrt-cube
1920×unpow-prod-down
1654×associate-*l*
1344×pow1
1031×cbrt-unprod
1030×associate-*r*
802×sqr-pow
743×difference-of-squares
551×add-log-exp
512×pow-unpow
461×cbrt-undiv
458×associate-/r*
456×associate-/l*
441×unswap-sqr
440×associate-*r/
430×pow-prod-down
419×div-inv
408×cbrt-prod
333×associate-*l/
308×sqrt-div
259×distribute-lft-out--
243×distribute-lft-out
234×frac-times
225×exp-prod
216×flip-+ flip3-+
170×flip3-- flip--
165×associate-/r/
152×*-commutative
142×cube-prod
116×sqrt-pow1
107×tan-quot
104×cbrt-div unpow2
88×frac-2neg clear-num
82×distribute-rgt-in distribute-lft-in
79×pow1/2
68×pow1/3
67×sub-neg
62×distribute-lft-neg-in distribute-rgt-neg-in
61×rem-sqrt-square
59×pow-pow
51×associate-/l/ pow-prod-up
36×frac-sub
35×div-sub
33×pow-sqr
32×sum-log swap-sqr
30×associate--l+
24×+-commutative log-prod
22×pow-plus
20×log-pow
17×pow2
16×diff-log frac-add
15×pow-sub
14×neg-mul-1
11×rem-exp-log
10×cube-div rem-cube-cbrt associate-+r+
9×exp-diff pow-flip
8×pow-neg associate-+r-
7×unpow3 inv-pow cube-mult
6×neg-sub0 acos-asin cos-sum rem-log-exp
5×sqrt-unprod exp-sum
4×asin-acos
3×cos-diff exp-to-pow
2×un-div-inv associate--l- associate-+l+ sub-div associate--r+ log-div
1×rem-square-sqrt mul0 exp-lft-cube

sample25.2s (3.6%)

Algorithm
37×intervals
Results
9.8s69290×body80valid
4.5s2777×body1280valid
2.5s17601×body80nan
2.3s2205×body640valid
673.0ms1174×body320valid
484.0ms281×body2560valid
392.0ms708×body160valid
386.0ms113×body5120valid
77.0ms128×body10240exit
11.0ms15×body1280nan
10.0ms19×body640nan
7.0ms18×body320nan
7.0ms256×pre80true
2.0ms8×body160nan

localize4.8s (0.7%)

regimes2.4s (0.3%)

Accuracy

Total 1.5b remaining (32.3%)

Threshold costs 1.5b (32.3%)

0.9b0%Bouland and Aaronson, Equation (26)
0.2b0%Maksimov and Kolovsky, Equation (32)
0.2b0%VandenBroeck and Keller, Equation (24)
0.1b0%Falkner and Boettcher, Appendix A
0.0b0%Bulmash initializePoisson

bsearch7.0ms (0.0%)

end0.0ms (0.0%)