Details

prune7.4m (39.8%)

simplify3.7m (20.0%)

sample3.2m (17.4%)

Algorithm
61×intervals
Results
41.8s253239×body80valid
40.1s29317×body1280valid
29.8s160933×body80nan
19.9s20690×body640valid
17.6s8872×body2560valid
11.9s3487×body5120valid
6.5s9713×body320valid
3.9s9130×body160valid
984.0ms829×body10240exit
656.0ms646×body640nan
404.0ms617×body1280nan
155.0ms8256×pre80true
133.0ms346×body320nan
84.0ms197×body160nan

series2.8m (15.1%)

Calls

432 calls:

8.4s
(sqrt (* (* (* 2.0 n) U) (* (* (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))) (cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t))))))
4.9s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))
4.8s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (* (/ l Om) l) (- 2.0) t))))
4.2s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))
4.0s
(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))

rewrite48.9s (4.4%)

Algorithm
115×rewrite-expression-head
Calls

432 calls:

7.7s
(* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n))))))
6.4s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (/ (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))) (/ (fma 2 1.0 (pow (/ k t) 2.0)) l)))
2.3s
(exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))
1.6s
(sqrt (+ (* (/ (pow (* M D) (/ 2.0 2)) (/ (cbrt l) (/ (pow (/ (/ 1 2.0) d) (/ 2.0 2)) (cbrt l)))) (* (/ (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (cbrt l)) (- h))) 1.0))
1.6s
(* (/ (/ (cbrt 2.0) (/ (pow (cbrt t) 3.0) (cbrt l))) (cbrt (sin k))) (* (/ (* (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l)))))) (* (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))) (/ (cbrt (/ (cbrt 2.0) (* (tan k) (/ (pow (cbrt t) 3.0) (cbrt l))))) (/ (cbrt (fma 2 1.0 (pow (/ k t) 2.0))) (cbrt l)))))
Rules
77793×times-frac
41941×add-exp-log
34360×add-sqr-sqrt
33105×*-un-lft-identity
32262×add-cube-cbrt
22573×prod-exp
19505×cbrt-prod
17992×div-exp
16893×unpow-prod-down
10022×pow-exp
8477×sqrt-prod
5874×associate-*l*
4134×pow-to-exp
4111×add-cbrt-cube
3330×sqr-pow
2718×cbrt-undiv
2267×associate-/r*
1941×cbrt-unprod
1765×div-inv
1654×1-exp
1646×rec-exp
1458×associate-*r*
1126×pow1
748×associate-/l*
488×add-log-exp
472×prod-diff
434×expm1-log1p-u
433×log1p-expm1-u
415×pow-unpow
396×difference-of-squares
329×unswap-sqr
319×pow-prod-down
294×distribute-rgt-neg-in
268×distribute-lft-neg-in
262×associate-/r/
257×distribute-lft-out--
256×exp-sum
220×distribute-lft-out
193×exp-prod associate-*r/
180×sqrt-pow1
110×*-commutative
102×pow1/2
101×frac-2neg clear-num
90×associate-*l/
86×sqrt-div tan-quot
81×pow1/3 distribute-rgt-in distribute-lft-in
78×rem-sqrt-square
71×frac-times
70×fma-def
54×neg-mul-1
47×pow-pow
45×swap-sqr flip-+ flip3-+
40×div-sub
39×flip3-- pow-prod-up associate-/l/ flip-- fma-udef
31×log-prod sub-neg
27×cos-sum
23×fma-neg pow-sub pow-sqr
20×pow-flip hypot-def
14×sum-log +-commutative
13×diff-log
12×pow-plus
10×inv-pow
associate-+r+ pow2 rem-exp-log
neg-sub0
exp-diff log-pow rem-log-exp
unpow2 distribute-frac-neg
cbrt-div un-div-inv
hypot-udef cube-div unpow-prod-up
associate-+l+ expm1-log1p expm1-udef exp-neg sqrt-unprod pow-neg rem-square-sqrt acos-asin
sin-sum associate-+r- sqrt-undiv distribute-rgt-neg-out log1p-expm1 neg-log sqrt-pow2 associate--r+ asin-acos unsub-neg associate--r- pow-div log1p-udef
frac-sub distribute-rgt-out-- mul0 pow3 sub-div cos-diff log-div

regimes24.4s (2.2%)

Accuracy

Total 39.5b remaining (20.5%)

Threshold costs 4.2b (2.2%)

9.3b15%Toniolo and Linder, Equation (13)
7.4b7.3%Henrywood and Agarwal, Equation (12)
5.4b77.5%Toniolo and Linder, Equation (7)
4.2b-8.6%Henrywood and Agarwal, Equation (9a)
3.5b29.3%Henrywood and Agarwal, Equation (13)

localize8.1s (0.7%)

bsearch4.8s (0.4%)

end1.0ms (0.0%)