Details

simplify26.6m (65.9%)

prune7.1m (17.5%)

sample4.3m (10.7%)

Algorithm
60×intervals
Results
1.0m248059×body80valid
52.1s27527×body1280valid
44.2s160919×body80nan
26.1s18640×body640valid
23.5s8652×body2560valid
15.3s3469×body5120valid
8.8s8890×body320valid
4.9s8566×body160valid
1.9s833×body10240exit
655.0ms623×body1280nan
510.0ms653×body640nan
299.0ms8256×pre80true
274.0ms344×body320nan
65.0ms184×body160nan

series1.4m (3.6%)

Calls

443 calls:

2.8s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ (/ l (* (cbrt Om) (cbrt Om))) (/ (cbrt Om) n)))))))))
2.3s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ (/ l (* (cbrt Om) (cbrt Om))) (/ (cbrt Om) n)))))))))
2.3s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ (/ l (* (cbrt Om) (cbrt Om))) (/ (cbrt Om) n)))))))))
2.3s
(sqrt (* (* (cbrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ (/ l (* (cbrt Om) (cbrt Om))) (/ (cbrt Om) n))))))))) (cbrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ (/ l (* (cbrt Om) (cbrt Om))) (/ (cbrt Om) n)))))))))) (cbrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ (/ l (* (cbrt Om) (cbrt Om))) (/ (cbrt Om) n)))))))))))
2.2s
(sqrt (* (* U n) (* 2 (- t (* (/ l Om) (- (* 2 l) (* (- U* U) (/ l (/ Om n)))))))))

rewrite27.7s (1.1%)

Algorithm
114×rewrite-expression-head
Calls

443 calls:

1.4s
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (pow (* (/ (cbrt d) (cbrt l)) (/ (cbrt d) (cbrt l))) 1/2) (pow (/ (cbrt d) (cbrt l)) 1/2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))
878.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l))))
856.0ms
(* (/ (* (/ (cbrt 2) (cbrt (sin k))) (/ (cbrt 2) (cbrt (sin k)))) (* (+ (* (/ k t) (/ k t)) 2) (* (/ (* (cbrt t) (cbrt t)) l) t))) (/ (/ (/ (cbrt 2) (cbrt (sin k))) (/ (cbrt t) (/ l t))) (tan k)))
803.0ms
(- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))
777.0ms
(* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (/ (* (* h (/ (/ M (/ d D)) 2)) (/ (/ M (/ d D)) 2)) (* 2 l))))
Rules
82680×times-frac
36071×add-sqr-sqrt
35766×*-un-lft-identity
34441×add-cube-cbrt
18724×cbrt-prod
13785×associate-*r*
11436×add-exp-log
8331×add-cbrt-cube
7265×sqrt-prod
4728×div-exp
4442×prod-exp
3845×cbrt-undiv
3643×cbrt-unprod
2477×div-inv
2243×unpow-prod-down
1374×pow1
1147×associate-*l*
1038×associate-/r*
929×associate-/l*
841×sqrt-div
755×sqr-pow
694×associate-*r/
687×difference-of-squares
668×associate-/r/
586×unpow-prod-up
556×frac-times
555×add-log-exp
467×flip-+ flip3-+
444×associate-*l/
443×insert-posit16
427×pow-prod-down
423×distribute-lft-out
370×unswap-sqr
340×sub-neg
302×flip3-- flip-- frac-add
293×pow-exp
156×1-exp
155×pow-to-exp
148×sqrt-pow1
138×*-commutative
137×cbrt-div
130×pow-unpow
107×frac-2neg clear-num
100×rec-exp
98×pow1/2
94×distribute-lft-out--
88×rem-sqrt-square
87×associate-/l/
73×swap-sqr
62×distribute-rgt-in distribute-lft-in
55×sin-mult
49×pow-prod-up
47×pow1/3
45×pow-sub
38×exp-prod
37×sum-log
30×pow-plus
29×pow-pow
25×+-commutative
23×log-pow diff-log
22×log-prod tan-quot
20×div-sub pow-sqr
17×pow2
9×associate-+r+
8×pow3 difference-of-sqr-1
6×pow-flip remove-posit16 inv-pow cos-sum rem-log-exp
5×acos-asin
4×exp-sum neg-log associate--r+ distribute-rgt-neg-in unpow2
3×associate-+r- frac-sub sqr-sin exp-to-pow asin-acos cos-diff
2×associate-+l+ neg-sub0 associate--l- cube-unmult associate--l+ rem-exp-log rem-cbrt-cube associate--r-
1×exp-diff sqrt-undiv sub-div sqrt-pow2 un-div-inv

regimes19.0s (0.8%)

Accuracy

Total 38.3b remaining (20.3%)

Threshold costs 4.8b (2.5%)

7.6b15.9%Toniolo and Linder, Equation (13)
7.1b16.2%Maksimov and Kolovsky, Equation (3)
5.2b77.7%Toniolo and Linder, Equation (7)
4.4b0%Henrywood and Agarwal, Equation (12)
3.3b13.8%Henrywood and Agarwal, Equation (13)

localize6.6s (0.3%)

bsearch2.4s (0.1%)

end1.0ms (0.0%)