Details

sample1.8m (48.7%)

Algorithm
21×intervals
Results
1.1m39558×body10240exit
11.2s7329×body1280valid
8.6s3478×body2560valid
7.2s57429×body80nan
6.3s56633×body80valid
3.2s4522×body640valid
1.1s2332×body320valid
374.0ms1206×body160valid
177.0ms8356×pre80true
127.0ms43×body5120valid
21.0ms26×body2560nan
17.0msbody5120nan
10.0ms23×body1280nan
8.0ms22×body640nan
3.0ms11×body320nan
2.0ms11×body160nan

simplify48.7s (21.8%)

series45.2s (20.2%)

Calls

87 calls:

6.0s
(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))))))
5.0s
(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))))
4.9s
(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))))
4.9s
(sqrt (* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t))))
2.6s
(cbrt (fma (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U* U)) (fma l (* (/ l Om) (- 2.0)) t)))

prune14.2s (6.4%)

regimes3.3s (1.5%)

Accuracy

Total 11.9b remaining (5.4%)

Threshold costs 0.5b (0.2%)

9.4b14.6%Toniolo and Linder, Equation (13)
2.0b0%Random Jason Timeout Test 006
0.4b0%Random Jason Timeout Test 012
0.0b0%Random Jason Timeout Test 004
0.0b0%Random Jason Timeout Test 003

localize1.3s (0.6%)

rewrite1.3s (0.6%)

Algorithm
27×rewrite-expression-head
Calls

87 calls:

104.0ms
(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))))))
83.0ms
(* (* (* 2.0 n) U) (fma (- U* U) (* n (pow (/ l Om) 2.0)) (fma (* (/ l Om) l) (- 2.0) t)))
83.0ms
(* (* (* 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)))
76.0ms
(* (* (cbrt n) (cbrt n)) (* (pow (/ l Om) (/ 2.0 2)) (cbrt n)))
73.0ms
(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))))
Rules
298×add-sqr-sqrt
262×*-un-lft-identity
230×add-cube-cbrt
226×pow1
180×add-exp-log
126×add-cbrt-cube
88×unpow-prod-down log1p-expm1-u
87×add-log-exp expm1-log1p-u
82×sqrt-prod
81×log-prod
68×pow-prod-down
66×unpow-prod-up
54×prod-diff
53×cbrt-prod
50×prod-exp associate-*r*
45×times-frac
44×sqrt-pow1
29×cbrt-unprod
27×pow-unpow
25×log-pow
24×exp-prod
22×pow1/2
18×pow-exp
17×pow1/3 pow-pow
16×difference-of-squares associate-*l* distribute-lft-out--
13×rem-log-exp
12×exp-sum unswap-sqr rem-sqrt-square sqr-pow pow-to-exp
fma-udef
*-commutative
sub-neg swap-sqr pow-sub
div-exp associate-/r* acos-asin associate-/l*
sqrt-pow2
distribute-lft-in rem-exp-log distribute-rgt-in div-inv log-div
expm1-udef pow-prod-up associate-/l/ pow-sqr flip3-- flip-- associate-/r/
exp-diff div-sub expm1-log1p cbrt-undiv frac-2neg pow2 pow-plus clear-num sin-diff

bsearch631.0ms (0.3%)

end0.0ms (0.0%)