Details

prune5.4m (28.8%)

simplify5.3m (28.3%)

sample3.3m (17.2%)

Algorithm
59×intervals
Results
43.9s243618×body80valid
36.1s29317×body1280valid
28.5s157721×body80nan
20.2s20690×body640valid
17.0s8872×body2560valid
10.0s3487×body5120valid
5.4s9713×body320valid
3.0s9130×body160valid
1.5s829×body10240exit
312.0ms646×body640nan
311.0ms617×body1280nan
280.0ms8256×pre80true
101.0ms346×body320nan
70.0ms197×body160nan

series3.1m (16.6%)

Calls

439 calls:

15.2s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
15.1s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
14.8s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
14.3s
(sqrt (* (* 2.0 n) (* (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om)))) U)))
14.0s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* n (pow (/ l Om) 2.0)) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))

rewrite1.1m (5.7%)

Algorithm
112×rewrite-expression-head
Calls

439 calls:

3.1s
(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
3.0s
(exp (- (- (fabs (- m n)) (pow (- (/ (+ m n) 2.0) M) 2.0)) l))
2.2s
(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1)))
2.2s
(cos (* (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (* (cbrt (* (cbrt (- (* (/ K 2.0) (+ m n)) M)) (cbrt (- (* (/ K 2.0) (+ m n)) M)))) (cbrt (cbrt (- (* (/ K 2.0) (+ m n)) M))))) (cbrt (- (* (/ K 2.0) (+ m n)) M))))
1.8s
(sqrt (* (* (* 2.0 n) (+ t (- (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U* U)) (* (* 2.0 l) (/ l Om))))) U))
Rules
62698×times-frac
30667×add-sqr-sqrt
29108×add-exp-log
27418×*-un-lft-identity
25809×add-cube-cbrt
18694×prod-exp
15693×sqrt-prod
15454×unpow-prod-down
9843×pow-exp
9237×div-exp
3477×add-cbrt-cube
3403×pow-to-exp
3162×associate-*r*
2990×sqr-pow
1831×div-inv
1685×associate-/l*
1640×1-exp
1570×sqrt-div
1557×pow1
1556×rec-exp
1417×associate-/r*
1400×cbrt-unprod
1254×associate-*l*
1196×unswap-sqr
1182×frac-times
878×cbrt-undiv
749×associate-*r/
624×associate-*l/
604×flip3-- flip--
539×cbrt-prod
521×add-log-exp
508×pow-prod-down
427×associate-/r/
333×pow-unpow
285×flip-+ flip3-+
274×difference-of-squares
263×distribute-lft-out
193×sqrt-pow1
187×distribute-lft-out--
141×*-commutative
119×pow1/2
97×frac-2neg clear-num pow-prod-up
88×exp-prod
83×rem-sqrt-square
77×cbrt-div
71×pow1/3
70×distribute-rgt-in distribute-lft-in
67×tan-quot
65×pow-sqr
63×swap-sqr
60×associate-/l/
56×sub-neg
55×frac-add
52×pow-pow div-sub
37×pow-plus
36×pow-sub
26×pow2
20×sum-log +-commutative diff-log
13×distribute-rgt-neg-in distribute-lft-neg-in
12×associate--l+ associate--r+
10×exp-sum
sqrt-unprod rem-exp-log
log-prod cube-div
pow-flip associate-+l+ sin-mult inv-pow
neg-sub0 pow-neg
exp-diff rem-square-sqrt
associate-+r- associate-+r+ cos-sum log-pow
rem-cube-cbrt difference-cubes unpow2 acos-asin
frac-sub pow3 rem-cbrt-cube distribute-rgt1-in
associate--l- unpow3 neg-mul-1 sub-div sqr-sin un-div-inv exp-to-pow cube-prod asin-acos cube-mult cos-diff rem-log-exp

regimes26.7s (2.4%)

Accuracy

Total 52.2b remaining (25%)

Threshold costs 4.8b (2.3%)

13.9b2.7%Henrywood and Agarwal, Equation (13)
8.9b29.3%Toniolo and Linder, Equation (13)
7.1b8.8%Henrywood and Agarwal, Equation (12)
5.5b77.2%Toniolo and Linder, Equation (7)
5.5b0%Maksimov and Kolovsky, Equation (3)

localize8.3s (0.7%)

bsearch3.1s (0.3%)

end1.0ms (0.0%)