Details

simplify3.9m (32.4%)

sample3.4m (28.1%)

Algorithm
61×intervals
Results
43.7s253510×body80valid
43.3s29904×body1280valid
29.5s159444×body80nan
18.8s8631×body2560valid
17.4s20118×body640valid
11.8s3441×body5120valid
6.4s9633×body320valid
2.9s8922×body160valid
1.0s635×body10240exit
731.0ms602×body640nan
372.0ms584×body1280nan
282.0ms8256×pre80true
142.0ms327×body320nan
34.0ms180×body160nan

series2.3m (19.1%)

Calls

440 calls:

7.5s
(sqrt (* (* 2.0 n) (* U (- (- t (* 2.0 (* l (/ l Om)))) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))
7.5s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
7.4s
(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*)))))
6.9s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))

prune1.4m (11.5%)

rewrite39.3s (5.4%)

Algorithm
116×rewrite-expression-head
Calls

440 calls:

1.4s
(* (* (* (/ (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))
1.1s
(* (* (* (/ (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) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
932.0ms
(/ (* (* (* (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) (* (/ l (pow (* (cbrt t) (cbrt t)) (/ 3.0 2))) (cos k)))
863.0ms
(+ (/ (* 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
44668×add-exp-log
32482×prod-exp
20237×pow-exp
14225×div-exp
9185×pow-to-exp
6197×times-frac
5937×add-sqr-sqrt
4490×*-un-lft-identity
3829×add-cube-cbrt
2871×sqrt-prod
2747×1-exp rec-exp
2496×add-cbrt-cube
1625×unpow-prod-down
1546×pow1
1320×associate-*r*
1013×cbrt-unprod
900×associate-*l*
563×difference-of-squares
537×sqr-pow
524×add-log-exp
463×pow-prod-down
444×cbrt-prod
421×unswap-sqr
415×cbrt-undiv
410×associate-*r/
403×associate-/r*
324×sqrt-div
323×associate-/l*
305×associate-*l/
287×pow-unpow
282×div-inv
237×frac-times
212×distribute-lft-out--
183×cube-prod
176×flip-+ flip3-+
168×flip-- flip3--
162×*-commutative
157×associate-/r/
136×pow-prod-up
127×distribute-lft-out
125×sqrt-pow1
109×distribute-rgt-in distribute-lft-in
108×cbrt-div
95×tan-quot
89×unpow2
83×pow1/3
82×clear-num frac-2neg
81×rem-sqrt-square
80×pow-sqr
78×sub-neg
72×pow-plus
66×pow1/2
59×associate-/l/
47×pow2
44×pow-pow
43×cube-div
37×div-sub
34×frac-sub
32×sum-log
28×+-commutative
26×pow-sub exp-prod
22×frac-add associate--l+
14×distribute-rgt-neg-in
13×distribute-lft-neg-in swap-sqr
12×unpow-prod-up pow-flip log-prod
11×unpow3 cube-mult
10×diff-log
9×inv-pow
7×rem-cube-cbrt associate-+l+
6×associate--r+
5×difference-cubes neg-sub0 acos-asin
4×cos-sum log-pow associate-+r+ pow-neg
3×un-div-inv associate-+r- distribute-rgt-out-- exp-sum rem-cbrt-cube
2×rem-exp-log pow3 cos-diff distribute-neg-frac neg-log asin-acos associate-+l- rem-log-exp
1×exp-diff sqrt-undiv sub-div neg-mul-1 mul0 sum-cubes

regimes15.7s (2.2%)

Accuracy

Total 48.6b remaining (21.7%)

Threshold costs 4.5b (2%)

10.8b11.2%Toniolo and Linder, Equation (13)
6.7b47.7%Henrywood and Agarwal, Equation (3)
5.6b8.4%Henrywood and Agarwal, Equation (12)
5.3b77.8%Toniolo and Linder, Equation (7)
5.0b27.4%Toniolo and Linder, Equation (10-)

bsearch5.3s (0.7%)

localize4.4s (0.6%)

end1.0ms (0.0%)