Details

simplify6.2m (41.2%)

sample3.5m (23.3%)

Algorithm
61×intervals
Results
46.2s252717×body80valid
42.3s29655×body1280valid
29.2s160168×body80nan
20.2s8843×body2560valid
20.1s19798×body640valid
11.1s3394×body5120valid
6.9s10182×body320valid
2.9s9191×body160valid
1.4s635×body10240exit
861.0ms619×body640nan
617.0ms8256×pre80true
512.0ms599×body1280nan
152.0ms361×body320nan
42.0ms209×body160nan

series2.8m (18.6%)

Calls

434 calls:

7.9s
(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)))) (* (* (cbrt (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))) (cbrt (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))) (cbrt (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))))
7.2s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

prune1.5m (10.2%)

rewrite37.3s (4.1%)

Algorithm
115×rewrite-expression-head
Calls

434 calls:

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))
1.5s
(+ (/ (* 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))))
1.4s
(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
1.4s
(exp (+ (pow (- (/ (+ m n) 2.0) M) 2.0) (- l (fabs (- m n)))))
1.2s
(* (* (* (/ (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
46971×add-exp-log
33120×prod-exp
21265×pow-exp
16217×div-exp
10207×pow-to-exp
7041×times-frac
6770×add-sqr-sqrt
5619×*-un-lft-identity
4853×sqrt-prod
4067×add-cube-cbrt
2355×add-cbrt-cube
1909×rec-exp 1-exp
1720×unpow-prod-down
1370×pow1
1122×difference-of-squares
1095×associate-*l*
911×cbrt-unprod
797×cbrt-prod
724×associate-*r*
561×sqr-pow
526×distribute-lft-out
515×add-log-exp
470×associate-/r*
451×cbrt-undiv
450×prod-diff
434×log1p-expm1-u expm1-log1p-u
396×associate-*r/
388×pow-prod-down
386×associate-*l/
370×pow-unpow div-inv
338×associate-/l*
276×distribute-lft-out--
242×sqrt-div
241×flip3-- flip--
233×frac-times
229×unswap-sqr
169×associate-/r/
150×distribute-rgt-in distribute-lft-in
146×sqrt-pow1
140×*-commutative
120×cbrt-div
111×tan-quot
108×pow-prod-up
104×cube-prod
90×frac-2neg clear-num
87×exp-prod
86×pow1/2
79×rem-sqrt-square frac-sub
73×pow1/3
72×fma-def
68×flip-+ flip3-+
62×pow-sqr
55×fma-neg
52×pow-plus
49×sub-neg
47×associate-/l/
45×distribute-lft-neg-in distribute-rgt-neg-in
42×pow-pow
41×swap-sqr
35×associate-+r+
34×fma-udef unpow2 pow2
32×associate--l+
31×div-sub
29×log-pow
28×sum-log
24×pow-sub cos-sum
18×unpow3 cube-mult
17×+-commutative
15×hypot-def
14×diff-log
9×rem-exp-log log-prod
8×associate-+r- frac-add
5×acos-asin exp-sum
4×exp-diff un-div-inv inv-pow pow-flip neg-sub0 neg-mul-1 pow-neg
3×rem-cube-cbrt sqrt-unprod hypot-udef
2×cube-div sqrt-undiv associate-+l+ pow3 rem-square-sqrt rem-cbrt-cube rem-log-exp
1×sqrt-pow2 e-exp-1 asin-acos sin-sum cos-diff unpow-prod-up distribute-rgt-out sub-div mul0

regimes15.7s (1.7%)

Accuracy

Total 36.5b remaining (18.8%)

Threshold costs 4.1b (2.1%)

9.3b16.5%Toniolo and Linder, Equation (13)
5.7b76.4%Toniolo and Linder, Equation (7)
4.1b57.5%Toniolo and Linder, Equation (10-)
3.5b28.6%Henrywood and Agarwal, Equation (12)
3.2b57.7%Toniolo and Linder, Equation (10+)

bsearch4.5s (0.5%)

localize4.0s (0.4%)

end1.0ms (0.0%)