Details

simplify3.7m (29.2%)

sample3.3m (25.5%)

Algorithm
61×intervals
Results
41.8s253108×body80valid
38.9s29608×body1280valid
28.6s161117×body80nan
21.0s19996×body640valid
16.5s8886×body2560valid
9.9s3399×body5120valid
5.7s9762×body320valid
3.1s8936×body160valid
1.3s902×body10240exit
738.0ms572×body1280nan
479.0ms8256×pre80true
361.0ms642×body640nan
104.0ms372×body320nan
81.0ms183×body160nan

series2.7m (21.2%)

Calls

451 calls:

15.6s
(sqrt (pow (* (* (* 2.0 n) (- t (- (* 2.0 (/ l (/ Om l))) (* (- (* n (pow (/ l Om) (* 2 (/ 2.0 2))))) (- U U*))))) U) 1))
7.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
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*)))))
6.7s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
3.0s
(cbrt (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))

prune1.8m (13.7%)

rewrite53.5s (7.0%)

Algorithm
119×rewrite-expression-head
Calls

451 calls:

2.7s
(* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.6s
(* (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) l)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.5s
(- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))
1.1s
(/ (- 1.0 (* 5.0 (* v v))) (* (/ (* PI (* t (sqrt (* 2.0 (- (pow 1.0 3) (pow (* 3.0 (* v v)) 3)))))) (sqrt (+ (* 1.0 1.0) (+ (* (* 3.0 (* v v)) (* 3.0 (* v v))) (* 1.0 (* 3.0 (* v v))))))) (- 1.0 (* v v))))
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
33818×add-exp-log
21446×prod-exp
12134×times-frac
11706×div-exp
10363×pow-exp
8852×add-sqr-sqrt
7833×*-un-lft-identity
6675×add-cube-cbrt
6184×sqrt-prod
3917×pow-to-exp
2866×add-cbrt-cube
2560×1-exp
2019×associate-*r*
1936×rec-exp
1525×associate-*l*
1328×pow1
1169×cbrt-unprod
871×unpow-prod-down
647×associate-/l*
602×unswap-sqr
575×associate-*r/
547×cbrt-undiv
535×add-log-exp
501×cbrt-prod
497×pow-unpow
458×distribute-lft-out--
456×pow-prod-down
451×div-inv
413×sqrt-div
398×associate-/r*
300×frac-times
290×sqr-pow associate-*l/
289×distribute-rgt-neg-in
285×exp-prod
278×distribute-lft-neg-in
271×difference-of-squares
224×associate-/r/
208×flip3-- flip--
204×sqrt-pow1
201×flip-+ flip3-+
187×distribute-lft-out
185×cbrt-div
169×*-commutative
97×clear-num frac-2neg
73×tan-quot
71×distribute-rgt-in distribute-lft-in
70×rem-sqrt-square
68×pow1/2
60×associate-/l/ sub-neg
59×unpow2
55×pow-pow
44×div-sub
40×frac-sub
39×pow1/3
38×neg-mul-1
31×neg-sub0
27×sum-log
25×pow-neg pow-sub
22×+-commutative
21×log-pow
20×frac-add
19×swap-sqr
18×exp-diff associate--l+
17×un-div-inv
16×cube-prod
15×diff-log
14×log-prod
13×associate-+r+ pow-flip
12×pow-sqr pow-prod-up
10×distribute-neg-frac
9×distribute-frac-neg
8×rem-log-exp log-div
7×inv-pow
6×associate-+r- sub-div unsub-neg acos-asin cos-sum
5×pow-plus associate-+l+ rem-exp-log exp-sum
4×unpow3 exp-neg distribute-neg-in cube-mult
3×sqrt-undiv pow2 cos-diff distribute-rgt-out-- neg-log
2×sqrt-unprod asin-acos associate--r+
1×associate--l- distribute-lft-neg-out associate--r- mul0 distribute-rgt-neg-out exp-to-pow

regimes15.3s (2.0%)

Accuracy

Total 46.2b remaining (22.5%)

Threshold costs 5.5b (2.7%)

11.6b8.1%Toniolo and Linder, Equation (13)
7.9b6%Toniolo and Linder, Equation (10+)
5.9b75.1%Toniolo and Linder, Equation (7)
5.2b8.6%Henrywood and Agarwal, Equation (12)
3.1b35.7%Toniolo and Linder, Equation (10-)

bsearch6.3s (0.8%)

localize4.5s (0.6%)

end1.0ms (0.0%)