Details

series7.5m (63.8%)

Calls

95 calls:

7.0m
(sin (* (pow 1 (- b a)) (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a)))))
4.9s
(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*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))
4.8s
(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*))))))

end2.9m (24.5%)

sample1.2m (9.8%)

Algorithm
21×intervals
Results
38.2s39173×body10240exit
7.3s7299×body1280valid
5.6s3426×body2560valid
4.9s58304×body80nan
4.8s56565×body80valid
2.3s4714×body640valid
693.0ms2332×body320valid
284.0ms1191×body160valid
172.0ms8356×pre80overflowed
67.0ms36×body5120valid
25.0ms11×body5120nan
13.0ms19×body2560nan
6.0ms18×body1280nan
3.0ms13×body320nan
2.0ms13×body640nan
2.0msbody160nan

prune6.6s (0.9%)

simplify3.4s (0.5%)

Algorithm
49×egg-herbie

regimes1.6s (0.2%)

Accuracy

Total 10.6b remaining (5%)

Threshold costs 0.5b (0.2%)

8.0b10%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 003
0.0b0%Random Jason Timeout Test 004

rewrite1.1s (0.2%)

Algorithm
31×rewrite-expression-head
Calls

95 calls:

88.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
65.0ms
(* (* (* 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*))))
60.0ms
(* (* (* 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*)))))
56.0ms
(* (cbrt (sin (expm1 a))) (* (* (cbrt (cbrt (sin (expm1 a)))) (cbrt (cbrt (sin (expm1 a))))) (cbrt (cbrt (sin (expm1 a))))))
52.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
Rules
472×add-sqr-sqrt
374×*-un-lft-identity
326×add-exp-log
294×unpow-prod-down
292×add-cube-cbrt
246×pow1
173×add-cbrt-cube
130×prod-exp
126×associate-*r* times-frac
121×sqrt-prod
100×cbrt-prod
97×add-log-exp
95×associate-*r/
67×pow-exp pow-prod-down
63×pow-unpow associate-*l*
52×unswap-sqr
50×flip-- flip3-- sqr-pow cbrt-unprod
41×sub-neg
40×unpow-prod-up distribute-lft-out-- pow-to-exp
36×pow1/3 log-prod
34×difference-of-squares
33×frac-sub sqrt-pow1
31×log-pow
30×swap-sqr
24×distribute-rgt-in sqrt-div distribute-lft-in
21×pow-pow
20×div-exp
19×exp-prod
18×associate-/r*
17×pow-prod-up
16×associate--l+
15×*-commutative pow1/2
12×cube-prod associate-/l*
11×div-inv
10×associate-/r/
pow-sub
sinh-def
pow-plus pow-sqr rem-log-exp
rem-sqrt-square
cbrt-undiv
cube-div cube-mult unpow3 clear-num frac-2neg pow2
sqrt-pow2 exp-sum distribute-rgt-out--
associate-/l/ cbrt-div rem-cube-cbrt distribute-rgt-out e-exp-1 acos-asin rem-cbrt-cube
diff-log div-sub frac-times rem-exp-log distribute-lft1-in associate-*l/ pow3 sub-div

localize407.0ms (0.1%)

bsearch102.0ms (0.0%)