8946 calls:
| 3.1s | (/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (* l 2) (* l 2)) (* l 2))) |
| 2.4s | (/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h))) |
| 2.1s | (/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2))) |
| 1.8s | (* (* (* (* (/ 2 (tan k)) (/ 2 (tan k))) (/ 2 (tan k))) (* (* (/ (/ (/ l t) 1) 1) (/ (/ (/ l t) 1) 1)) (/ (/ (/ l t) 1) 1))) (/ (* (* (/ (/ l t) (+ 2 (* (/ k t) (/ k t)))) (/ (/ l t) (+ 2 (* (/ k t) (/ k t))))) (/ (/ l t) (+ 2 (* (/ k t) (/ k t))))) (* (* (* t (sin k)) (* t (sin k))) (* t (sin k))))) |
| 1.8s | (/ (* (* (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2)))) (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2))))) (* (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (* (* -2 J) (cos (/ K 2))))) (* (* (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))) (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))) |
| 56× | intervals |
| 58.7s | 247085× | body | 80 | valid |
| 47.8s | 23889× | body | 1280 | valid |
| 41.2s | 159773× | body | 80 | nan |
| 25.2s | 18424× | body | 640 | valid |
| 20.4s | 8728× | body | 10240 | exit |
| 18.1s | 7217× | body | 2560 | valid |
| 15.6s | 3457× | body | 5120 | valid |
| 8.9s | 8922× | body | 320 | valid |
| 5.0s | 8882× | body | 160 | valid |
| 576.0ms | 609× | body | 1280 | nan |
| 545.0ms | 679× | body | 640 | nan |
| 241.0ms | 345× | body | 320 | nan |
| 103.0ms | 192× | body | 160 | nan |
425 calls:
| 1.4s | (cos (* (* (cbrt (- (/ K (/ 2 (+ m n))) M)) (cbrt (* m (/ K 2)))) (cbrt (- (/ K (/ 2 (+ m n))) M)))) |
| 1.2s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.1s | (sqrt (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) |
| 1.1s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.1s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
Total 44.5b remaining (25.3%)
| 7.5b | 12.2% | Maksimov and Kolovsky, Equation (3) |
| 6.3b | 33.2% | Toniolo and Linder, Equation (13) |
| 6.2b | -3.3% | Henrywood and Agarwal, Equation (13) |
| 5.6b | 77.9% | Toniolo and Linder, Equation (7) |
| 4.0b | 53.1% | Henrywood and Agarwal, Equation (3) |
| 108× | rewrite-expression-head |
425 calls:
| 369.0ms | (sqrt (+ 1 (/ (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (/ Om l) (/ 4 (/ Om l)))))) |
| 306.0ms | (* (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))) (/ (* (* -2 J) (cos (/ K 2))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1))))))) |
| 182.0ms | (sqrt (* (* (* (* 2 n) U) (* (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) (cbrt (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*)))))) |
| 135.0ms | (cbrt (* (* (* (+ (* a a) (* b b)) (+ (* a a) (* b b))) (* (+ (* a a) (* b b)) (+ (* a a) (* b b)))) (* (+ (* a a) (* b b)) (+ (* a a) (* b b))))) |
| 128.0ms | (/ (sqrt (+ 1 (* (* (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J)) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))) (* (/ (/ U (* 2 (cos (/ K 2)))) J) (/ (/ U (* 2 (cos (/ K 2)))) J))))) (sqrt (sqrt (+ (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J))))) (- (* 1 1) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)))))) |
| 3246× | frac-times |
| 3087× | times-frac |
| 2293× | add-sqr-sqrt |
| 2253× | *-un-lft-identity |
| 2148× | add-cube-cbrt |
| 2103× | associate-*r/ |
| 1708× | flip-+ flip3-+ |
| 1690× | cbrt-div |
| 1185× | add-exp-log |
| 1177× | associate-*l/ |
| 1058× | flip3-- flip-- |
| 1019× | add-cbrt-cube |
| 925× | sqrt-div |
| 737× | pow1 |
| 693× | associate-*l* |
| 669× | div-inv |
| 665× | associate-*r* |
| 639× | sqrt-prod |
| 634× | frac-sub |
| 507× | cbrt-prod |
| 490× | associate-/r/ |
| 489× | add-log-exp |
| 425× | insert-posit16 |
| 333× | associate-/r* |
| 287× | associate-/l* frac-add |
| 255× | prod-exp |
| 212× | div-exp |
| 203× | cbrt-unprod |
| 188× | cbrt-undiv |
| 145× | *-commutative |
| 136× | unpow-prod-down |
| 117× | pow-prod-down |
| 109× | frac-2neg clear-num |
| 88× | associate-/l/ |
| 71× | pow1/2 |
| 69× | distribute-rgt-in distribute-lft-in |
| 63× | rem-sqrt-square |
| 56× | sub-neg |
| 50× | pow1/3 |
| 47× | cube-prod |
| 45× | difference-of-squares pow-to-exp |
| 43× | div-sub |
| 40× | pow2 |
| 38× | rec-exp |
| 33× | pow-prod-up |
| 28× | pow-unpow |
| 27× | distribute-lft-out associate-+r+ pow-sub |
| 26× | distribute-lft-out-- |
| 25× | sum-log tan-quot |
| 24× | pow-exp pow-plus |
| 21× | exp-prod |
| 20× | associate--l+ +-commutative |
| 19× | pow-pow |
| 17× | pow-flip |
| 15× | log-prod |
| 13× | inv-pow |
| 12× | unpow2 |
| 8× | difference-of-sqr-1 diff-log |
| 6× | distribute-lft-neg-in distribute-rgt-neg-in asin-acos |
| 5× | exp-diff associate-+r- rem-exp-log |
| 4× | distribute-frac-neg neg-sub0 difference-cubes distribute-neg-frac log-pow |
| 3× | sin-mult sqr-sin associate-+l- distribute-rgt-out |
| 2× | associate-+l+ rem-cube-cbrt sqrt-undiv distribute-rgt-out-- pow-div pow3 unpow3 neg-mul-1 rem-log-exp exp-neg cos-sum rem-cbrt-cube cube-mult |
| 1× | sub-div associate--l- cube-div acos-asin cos-diff associate--r- |