Details

simplify3.7m (31.1%)

sample3.3m (28.2%)

Algorithm
61×intervals
Results
44.8s253197×body80valid
41.3s29526×body1280valid
27.4s160776×body80nan
18.9s8730×body2560valid
17.7s20109×body640valid
9.9s3246×body5120valid
7.2s9991×body320valid
3.4s9054×body160valid
1.0s780×body10240exit
389.0ms651×body1280nan
300.0ms617×body640nan
170.0ms8256×pre80true
85.0ms314×body320nan
32.0ms174×body160nan

series2.4m (19.9%)

Calls

428 calls:

7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*)))))
7.4s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
6.7s
(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 (/ Om l)))) (* (* (* (cbrt n) (cbrt n)) (* (cbrt n) (pow (/ l Om) 2.0))) (- U U*))))

prune1.3m (11.2%)

rewrite43.9s (6.2%)

Algorithm
113×rewrite-expression-head
Calls

428 calls:

8.6s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
1.8s
(* (* (* (/ (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))
1.3s
(+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (* (* (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D))))) (cbrt (/ (* c0 (* d d)) (* (* w h) (* D D)))))) (* M M))))
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))
1.1s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
Rules
42282×add-exp-log
30868×prod-exp
22965×pow-exp
16241×div-exp
11318×pow-to-exp
4902×times-frac
4452×add-sqr-sqrt
3829×*-un-lft-identity
3604×rec-exp 1-exp
3495×add-cube-cbrt
2264×add-cbrt-cube
1615×sqrt-prod
1377×unpow-prod-down
1133×pow1
944×associate-*r*
909×cbrt-unprod
825×cbrt-prod
735×associate-*l*
512×add-log-exp
440×associate-*r/
431×associate-/r*
414×sqr-pow
403×cbrt-undiv
391×pow-unpow
383×associate-/l*
345×pow-prod-down
339×unswap-sqr
306×div-inv
277×sqrt-div
231×associate-*l/
172×associate-/r/
168×flip-+ flip3-+
151×frac-times
142×*-commutative
136×difference-of-squares flip3-- flip--
121×sqrt-pow1
113×unpow2
105×tan-quot
99×distribute-lft-out--
96×distribute-lft-out
92×clear-num frac-2neg
88×distribute-rgt-in distribute-lft-in
83×pow1/2
69×sub-neg
68×pow1/3
62×rem-sqrt-square
59×swap-sqr
55×pow-pow
52×cube-prod
47×cbrt-div
46×frac-add
42×exp-prod
41×frac-sub
34×sum-log
32×cube-div
29×associate-/l/
24×log-pow +-commutative associate--l+
19×unpow3 cube-mult
18×pow-prod-up div-sub
14×pow-sqr distribute-rgt-neg-in
13×distribute-lft-neg-in
12×rem-cube-cbrt
10×diff-log pow-sub
associate-+l+ associate-+r+ associate--r+
cos-sum un-div-inv inv-pow pow-flip
pow-plus neg-sub0 pow2
acos-asin pow-neg
cos-diff exp-sum log-prod rem-cbrt-cube
exp-diff unpow1/3 sqrt-unprod neg-log distribute-neg-frac rem-square-sqrt asin-acos associate-+l-
rem-exp-log associate-+r- associate--l- neg-mul-1 associate--r- mul0 rem-log-exp

regimes16.5s (2.3%)

Accuracy

Total 47.1b remaining (21.2%)

Threshold costs 6.8b (3.1%)

9.6b22.8%Toniolo and Linder, Equation (13)
7.3b69.1%Toniolo and Linder, Equation (7)
7.3b42.1%Henrywood and Agarwal, Equation (3)
5.2b29.5%Toniolo and Linder, Equation (10-)
5.1b0%Henrywood and Agarwal, Equation (12)

localize4.1s (0.6%)

bsearch3.4s (0.5%)

end1.0ms (0.0%)