28442 calls:
| 2.3s | (* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J))))) |
| 2.2s | (* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J))))) |
| 2.1s | (* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (* (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) (/ U (* 2 (* (cos (/ K 2)) J))))) |
| 2.0s | (* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J))))) |
| 2.0s | (* (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) (cos (/ K 2))) (cos (/ K 2))) (* (* J J) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J))))) |
| 87× | rewrite-expression-head |
338 calls:
| 44.1s | (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) (cbrt J)) |
| 18.3s | (* (* J (+ (* l (+ (log (exp (* l (* 1/3 l)))) 2)) (* (pow l 5) 1/60))) (cos (/ K 2))) |
| 11.5s | (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) (* (cbrt J) (cbrt J)))) |
| 11.1s | (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (* (cos (/ K 2)) J)) |
| 8.3s | (* (* J (+ (* l (+ (* l (* 1/3 l)) 2)) (* (pow l 5) 1/60))) (cos (/ K 2))) |
| 3119808× | times-frac |
| 1487253× | add-sqr-sqrt |
| 1250498× | *-un-lft-identity |
| 1230581× | add-cube-cbrt |
| 277091× | associate-/r/ |
| 263572× | associate-*l* |
| 261410× | associate-*r* |
| 244609× | swap-sqr |
| 236975× | frac-times |
| 181024× | associate-/l* |
| 170505× | associate-/r* |
| 127479× | div-inv |
| 90540× | unswap-sqr |
| 55483× | clear-num |
| 52766× | frac-2neg |
| 37496× | tan-quot |
| 29829× | associate-*r/ |
| 29202× | associate-*l/ |
| 21970× | *-commutative |
| 19403× | sqrt-prod |
| 15909× | sqrt-div |
| 12004× | cbrt-prod |
| 9341× | frac-add |
| 8824× | associate-/l/ |
| 6620× | distribute-lft-out |
| 5459× | un-div-inv |
| 4941× | unpow-prod-down |
| 4662× | flip3-- flip-- |
| 4240× | flip-+ flip3-+ |
| 4057× | difference-of-squares |
| 3938× | add-exp-log |
| 3274× | add-cbrt-cube |
| 1418× | prod-exp |
| 1402× | frac-sub |
| 1380× | div-exp |
| 1255× | sqr-pow |
| 1208× | cbrt-unprod |
| 1152× | pow1 |
| 1114× | cbrt-undiv |
| 887× | distribute-lft-out-- |
| 634× | sin-mult |
| 545× | cbrt-div |
| 382× | add-log-exp |
| 360× | pow-prod-down |
| 338× | insert-posit16 |
| 276× | rem-sqrt-square |
| 186× | pow-exp |
| 145× | pow-unpow |
| 108× | distribute-rgt-in distribute-lft-in |
| 90× | difference-of-sqr-1 |
| 87× | pow-to-exp |
| 86× | sqrt-pow1 |
| 70× | pow1/2 |
| 69× | log-pow |
| 63× | unpow2 sub-neg |
| 56× | exp-prod |
| 52× | +-commutative |
| 50× | 1-exp rec-exp |
| 46× | pow-prod-up |
| 41× | pow1/3 |
| 32× | associate-+l+ div-sub |
| 28× | distribute-lft-neg-in distribute-rgt-neg-in |
| 24× | pow-pow pow-sqr |
| 23× | pow-sub |
| 22× | associate-+r+ pow-plus |
| 19× | pow2 |
| 16× | distribute-rgt-out-- |
| 14× | associate--l+ |
| 13× | distribute-rgt-out |
| 11× | sum-log diff-log |
| 9× | log-prod |
| 8× | sqr-sin |
| 7× | sub-div |
| 6× | pow-flip distribute-lft1-in remove-double-div pow3 cos-sum rem-log-exp |
| 5× | inv-pow |
| 4× | associate--r+ neg-mul-1 acos-asin |
| 3× | associate-+r- cos-diff |
| 2× | exp-to-pow distribute-neg-frac asin-acos e-exp-1 |
| 1× | neg-sub0 remove-posit16 sqrt-undiv distribute-frac-neg associate--l- sqrt-pow2 associate-+l- unpow1/3 |
| 44× | intervals |
| 31.5s | 149476× | body | 80 | valid |
| 27.1s | 15788× | body | 1280 | valid |
| 18.7s | 8132× | body | 10240 | exit |
| 15.6s | 12326× | body | 640 | valid |
| 10.2s | 49890× | body | 80 | nan |
| 6.0s | 6222× | body | 320 | valid |
| 3.9s | 7670× | body | 160 | valid |
| 3.8s | 3188× | body | 2560 | valid |
| 622.0ms | 563× | body | 1280 | nan |
| 560.0ms | 657× | body | 640 | nan |
| 303.0ms | 87× | body | 5120 | valid |
| 204.0ms | 336× | body | 320 | nan |
| 149.0ms | 207× | body | 160 | nan |
338 calls:
| 28.1s | (sqrt (* (* (cbrt (* 2 n)) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 15.5s | (sqrt (* (cbrt (* (cbrt (* 2 n)) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 15.2s | (sqrt (* (cbrt (* (cbrt (* 2 n)) U)) (- (- t (* (/ l (/ Om l)) 2)) (* (* (* (/ l Om) (/ l Om)) n) (- U U*))))) |
| 1.6s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.5s | (* (* (cbrt (* 2 n)) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*)))) |
Total 14.1b remaining (41.1%)
| 8.6b | 68% | Toniolo and Linder, Equation (7) |
| 2.0b | 0% | Toniolo and Linder, Equation (3b), real |
| 1.6b | 0% | Henrywood and Agarwal, Equation (3) |
| 0.4b | 0% | Maksimov and Kolovsky, Equation (4) |
| 0.4b | 0% | Migdal et al, Equation (64) |