Details

simplify5.2m (29.2%)

sample4.3m (24.5%)

Algorithm
61×intervals
Results
55.4s252948×body80valid
53.5s29784×body1280valid
35.0s160481×body80nan
24.3s20236×body640valid
24.2s8721×body2560valid
15.0s3469×body5120valid
7.7s9840×body320valid
4.6s8802×body160valid
1.5s609×body10240exit
521.0ms613×body640nan
504.0ms607×body1280nan
286.0ms8256×pre80true
142.0ms378×body320nan
47.0ms186×body160nan

series4.1m (23.4%)

Calls

435 calls:

22.6s
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (- U U*) (* n (pow (/ l Om) 2.0))))) U)))
22.1s
(sqrt (* (* 2.0 n) (* (- t (fma (* l (/ l Om)) 2.0 (* (* (- U U*) n) (pow (/ l Om) 2.0)))) U)))
9.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
9.1s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.1s
(/ (* 1.0 (pow (pow (* (* 2.0 PI) n) (+ (sqrt 1.0) (sqrt k))) (/ (- (sqrt 1.0) (sqrt k)) 2.0))) (sqrt k))

prune2.7m (15.1%)

rewrite42.6s (4.0%)

Algorithm
115×rewrite-expression-head
Calls

435 calls:

2.3s
(* (* (* (/ (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))
2.0s
(+ (/ (* 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))))
1.6s
(* (* (* (/ (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))
1.4s
(* (* (* (pow (cbrt t) 3.0) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (sin k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
1.2s
(+ (/ (* 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
45249×add-exp-log
33593×prod-exp
24481×pow-exp
16748×div-exp
11857×pow-to-exp
6387×times-frac
4881×add-sqr-sqrt
4472×*-un-lft-identity
4160×add-cube-cbrt
3903×1-exp rec-exp
2731×sqrt-prod
2269×add-cbrt-cube
1560×unpow-prod-down
1288×cbrt-prod
1143×pow1
946×associate-*l*
876×cbrt-unprod
645×associate-*r*
495×add-log-exp
492×div-inv
436×expm1-log1p-u
435×log1p-expm1-u
420×associate-/l*
419×cbrt-undiv
414×associate-/r*
350×pow-prod-down
344×sqr-pow prod-diff
327×pow-unpow
275×associate-*r/
250×associate-*l/
211×unswap-sqr
178×exp-prod
163×log-pow
154×sqrt-div
153×frac-times
142×sqrt-pow1
129×difference-of-squares
124×associate-/r/
123×flip3-- flip--
121×*-commutative
105×pow1/3
99×distribute-lft-out--
98×distribute-rgt-in distribute-lft-in clear-num frac-2neg
93×tan-quot
78×distribute-lft-out
62×fma-def
61×flip-+ flip3-+
58×swap-sqr
53×pow1/2
51×fma-neg
48×pow-pow
47×cos-sum
43×unpow2 sub-neg
41×associate-/l/ distribute-rgt-neg-in
40×distribute-lft-neg-in log-prod
38×rem-sqrt-square
33×cbrt-div
32×fma-udef
25×cube-prod
22×associate-+r+ associate--l+
21×div-sub
18×pow-sub sum-log frac-sub
14×pow-prod-up pow-sqr
12×+-commutative hypot-def
11×diff-log pow-flip
9×un-div-inv rem-log-exp
8×inv-pow
7×pow-plus pow2 asin-acos
6×unpow3 cube-mult neg-sub0
5×rem-exp-log pow-neg exp-sum
4×cube-div rem-cube-cbrt frac-add neg-mul-1 associate-+r- log-div
3×exp-diff unpow-prod-up distribute-rgt-out--
2×sqrt-pow2 cos-diff exp-to-pow
1×neg-log sqrt-undiv associate-+l+ log1p-udef sqrt-unprod sin-sum log1p-expm1 expm1-log1p hypot-udef unsub-neg acos-asin sub-div associate--r- mul0 rem-cbrt-cube expm1-udef

regimes30.1s (2.8%)

Accuracy

Total 49.0b remaining (23%)

Threshold costs 5.0b (2.4%)

9.6b27.5%Toniolo and Linder, Equation (13)
7.3b5.5%Toniolo and Linder, Equation (10-)
6.8b0%Henrywood and Agarwal, Equation (12)
5.9b75.9%Toniolo and Linder, Equation (7)
5.8b54.3%Henrywood and Agarwal, Equation (3)

localize7.7s (0.7%)

bsearch3.3s (0.3%)

end1.0ms (0.0%)