28028 calls:
| 13.1s | (/ (* (cbrt (pow k m)) (cbrt (pow k m))) 1) |
| 10.7s | (sqrt (+ 1 (* (* (sqrt (/ h l)) (/ (* (sqrt M) (sqrt D)) (sqrt (* 2 d)))) (/ (sqrt (* M D)) (* (sqrt 2) (sqrt d)))))) |
| 10.4s | (* (/ h (sqrt l)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) |
| 1.4s | (* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) |
| 1.3s | (* (/ (* (* h h) h) (* (* l l) l)) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) |
| 86× | rewrite-expression-head |
328 calls:
| 1.8m | (sqrt (- 1 (* (/ (* (* (cbrt h) (cbrt h)) (/ (* M D) (* (cbrt (* 2 d)) (cbrt (* 2 d))))) (* (/ l (cbrt h)) (cbrt (* 2 d)))) (/ (* M D) (* 2 d))))) |
| 39.7s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 29.2s | (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) |
| 3.8s | (cos (- (* (* (/ K 2) (* (cbrt (+ m n)) (cbrt (+ m n)))) (cbrt (+ m n))) M)) |
| 3.8s | (/ (/ (/ (/ 2 (sin k)) (/ t (* (/ l t) (/ l t)))) (tan k)) (* (/ k t) (/ k t))) |
| 3033849× | times-frac |
| 1933043× | add-sqr-sqrt |
| 1175972× | *-un-lft-identity |
| 1153056× | add-cube-cbrt |
| 391617× | unswap-sqr |
| 319603× | associate-*r* |
| 292104× | associate-*l* |
| 253770× | swap-sqr |
| 233281× | cbrt-prod |
| 211837× | associate-/r/ |
| 201384× | frac-times |
| 167967× | associate-/l* |
| 155870× | associate-/r* |
| 106679× | div-inv |
| 57281× | sqrt-prod |
| 53536× | associate-*r/ |
| 49681× | sqrt-div |
| 46358× | clear-num |
| 44268× | frac-2neg |
| 39572× | *-commutative |
| 35707× | difference-of-squares |
| 20280× | associate-*l/ |
| 7746× | unpow-prod-down |
| 6527× | associate-/l/ |
| 5126× | sqr-pow |
| 4884× | add-cbrt-cube |
| 4715× | prod-diff |
| 4359× | add-exp-log |
| 4184× | un-div-inv |
| 2772× | cbrt-unprod |
| 2242× | fma-def |
| 2222× | frac-add |
| 2107× | prod-exp |
| 1830× | cbrt-undiv |
| 1310× | flip-- flip3-- |
| 1265× | div-exp |
| 1231× | pow1 |
| 1060× | cos-sum |
| 1018× | distribute-lft-out-- |
| 842× | distribute-rgt-in distribute-lft-in |
| 608× | cbrt-div |
| 530× | distribute-lft-out |
| 396× | pow-prod-down |
| 395× | associate--l+ |
| 358× | add-log-exp |
| 349× | frac-sub |
| 330× | log1p-expm1-u |
| 328× | expm1-log1p-u |
| 327× | insert-posit16 |
| 266× | pow-exp |
| 240× | pow-to-exp |
| 210× | distribute-lft-neg-in distribute-rgt-neg-in |
| 196× | tan-quot |
| 166× | exp-prod |
| 120× | fma-neg |
| 116× | pow-prod-up |
| 104× | difference-of-sqr-1 |
| 100× | rem-sqrt-square |
| 87× | div-sub |
| 82× | flip-+ pow1/3 flip3-+ |
| 81× | unpow2 |
| 66× | pow-sqr |
| 63× | pow-sub |
| 56× | pow-unpow |
| 55× | sqrt-pow1 |
| 50× | pow-plus |
| 44× | pow-flip |
| 40× | 1-exp |
| 39× | pow1/2 |
| 38× | pow2 fma-udef |
| 30× | neg-mul-1 |
| 22× | +-commutative |
| 21× | sub-neg |
| 20× | rec-exp |
| 12× | exp-diff associate--r+ distribute-neg-frac |
| 9× | pow-pow |
| 8× | diff-log |
| 7× | associate-+l+ sub-div inv-pow |
| 6× | expm1-log1p neg-sub0 sum-log distribute-frac-neg |
| 5× | distribute-rgt-out-- |
| 4× | pow-div |
| 3× | expm1-udef associate-+r- asin-acos rem-exp-log cos-diff |
| 2× | remove-double-div cube-unmult exp-neg hypot-udef acos-asin |
| 1× | remove-posit16 sqrt-undiv log1p-expm1 sqr-sin sin-mult log1p-udef |
| 44× | intervals |
| 36.4s | 155010× | body | 80 | valid |
| 19.6s | 12789× | body | 1280 | valid |
| 18.4s | 8118× | body | 10240 | exit |
| 12.1s | 52009× | body | 80 | nan |
| 10.9s | 9634× | body | 640 | valid |
| 5.3s | 4894× | body | 320 | valid |
| 3.4s | 3189× | body | 2560 | valid |
| 3.1s | 6807× | body | 160 | valid |
| 434.0ms | 94× | body | 5120 | valid |
| 23.0ms | 18× | body | 1280 | nan |
| 18.0ms | 19× | body | 640 | nan |
| 9.0ms | 13× | body | 320 | nan |
| 5.0ms | 10× | body | 160 | nan |
328 calls:
| 6.5s | (sqrt (* (* (cbrt (* (* n (sqrt 2)) U)) (cbrt (sqrt 2))) (- (fma (/ (* l l) Om) -2 t) (* (* (- U U*) (* n (/ l Om))) (/ l Om))))) |
| 5.7s | (sqrt (* (* (cbrt (sqrt 2)) (cbrt (* (* (sqrt 2) n) U))) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 4.7s | (sqrt (* (cbrt (* (* 2 n) U)) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.5s | (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) |
Total 6.8b remaining (24%)
| 3.9b | 0% | Maksimov and Kolovsky, Equation (3) |
| 0.9b | 0% | Toniolo and Linder, Equation (3a) |
| 0.4b | 0% | Bouland and Aaronson, Equation (25) |
| 0.4b | 0% | Migdal et al, Equation (64) |
| 0.3b | 0% | Maksimov and Kolovsky, Equation (4) |