14937 calls:
| 2.3s | (/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (/ (* (* (sin k) (sin k)) (sin k)) (/ (* (* l l) l) (* (* t t) t)))) (* (* (cos k) (cos k)) (cos k)))) |
| 2.2s | (* (* (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))))) (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om))))) (* (* (- U U*) (- U U*)) (- U U*))) |
| 2.2s | (/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 2)) (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (sin k)) (sin k)) (* (* (tan k) (tan k)) (tan k))) (/ (* (* t t) t) (* (* (* (/ l t) (/ l t)) (/ l t)) (* (* (/ l t) (/ l t)) (/ l t)))))) |
| 2.1s | (* (* (* (* 2 2) 2) (* (* n n) n)) (* (* (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))))) |
| 2.0s | (/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (/ (sin k) (/ l t)) (/ (sin k) (/ l t))) (/ (sin k) (/ l t)))) (* (* (cos k) (cos k)) (cos k)))) |
| 54× | intervals |
| 1.0m | 239242× | body | 80 | valid |
| 41.3s | 158766× | body | 80 | nan |
| 31.7s | 18116× | body | 1280 | valid |
| 20.8s | 8655× | body | 10240 | exit |
| 18.0s | 14018× | body | 640 | valid |
| 7.6s | 4963× | body | 2560 | valid |
| 6.1s | 2348× | body | 5120 | valid |
| 5.8s | 7012× | body | 320 | valid |
| 4.8s | 8102× | body | 160 | valid |
| 666.0ms | 637× | body | 1280 | nan |
| 601.0ms | 623× | body | 640 | nan |
| 224.0ms | 343× | body | 320 | nan |
| 68.0ms | 195× | body | 160 | nan |
386 calls:
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.7s | (sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*)))))) |
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) 2)) (* (/ (cbrt l) (cbrt Om)) (/ (cbrt l) (cbrt Om)))) (- U U*))))) |
| 1.6s | (* (fma (/ h l) (* -1/2 (* (/ M (/ (* 2 d) D)) (/ M (/ (* 2 d) D)))) 1) (* (* (fabs (cbrt d)) (sqrt (/ (cbrt d) l))) (* (fabs (/ (cbrt d) (cbrt h))) (sqrt (/ (cbrt d) (cbrt h)))))) |
| 1.6s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 103× | rewrite-expression-head |
386 calls:
| 4.2s | (* (/ c0 (* w 2)) (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w))) |
| 1.9s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 1.9s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 1.8s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 1.8s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 23668× | times-frac |
| 12347× | add-sqr-sqrt |
| 11835× | *-un-lft-identity |
| 10710× | add-cube-cbrt |
| 4424× | add-exp-log |
| 3612× | sqrt-prod |
| 3253× | add-cbrt-cube |
| 1940× | pow1 |
| 1719× | associate-*r* |
| 1693× | prod-exp |
| 1431× | div-exp |
| 1172× | cbrt-undiv |
| 1163× | div-inv |
| 1153× | associate-/l* |
| 1037× | cbrt-unprod |
| 1006× | prod-diff |
| 849× | associate-*l* |
| 811× | associate-/r/ |
| 712× | cbrt-prod |
| 625× | associate-*r/ |
| 614× | difference-of-squares |
| 544× | pow-prod-down |
| 541× | associate-/r* |
| 417× | add-log-exp |
| 386× | expm1-log1p-u insert-posit16 log1p-expm1-u |
| 383× | unpow-prod-down |
| 362× | frac-times |
| 336× | pow-prod-up |
| 301× | unswap-sqr |
| 300× | associate-*l/ |
| 275× | flip3-- flip-- |
| 273× | distribute-lft-out-- |
| 255× | pow-unpow |
| 205× | distribute-rgt-in distribute-lft-in |
| 203× | distribute-lft-out |
| 168× | sqr-pow |
| 151× | pow-sqr |
| 137× | pow-exp |
| 136× | sqrt-div |
| 132× | *-commutative |
| 128× | pow-plus |
| 112× | distribute-lft-neg-in distribute-rgt-neg-in |
| 108× | frac-sub |
| 94× | frac-2neg clear-num |
| 91× | pow2 |
| 79× | flip-+ flip3-+ |
| 76× | sqrt-pow1 |
| 70× | swap-sqr rem-sqrt-square |
| 62× | 1-exp rec-exp pow1/2 |
| 60× | pow-to-exp |
| 57× | fma-neg |
| 56× | associate--l+ |
| 54× | sub-neg |
| 53× | fma-udef |
| 49× | fma-def |
| 37× | associate-/l/ |
| 36× | tan-quot |
| 27× | pow-pow |
| 22× | exp-prod |
| 20× | pow1/3 div-sub |
| 19× | cube-unmult |
| 18× | frac-add |
| 16× | neg-mul-1 |
| 12× | cos-sum |
| 11× | pow-flip |
| 9× | cbrt-div inv-pow unpow2 pow-sub |
| 8× | sum-log +-commutative distribute-neg-frac |
| 7× | diff-log |
| 6× | hypot-udef |
| 5× | remove-posit16 sin-sum |
| 4× | neg-sub0 associate-+r+ difference-of-sqr-1 un-div-inv distribute-frac-neg acos-asin |
| 3× | associate-+r- sin-mult sqr-sin asin-acos |
| 2× | hypot-def cos-diff |
| 1× | associate-+l+ expm1-log1p expm1-udef exp-diff pow3 sub-div sqrt-pow2 rem-exp-log sin-diff distribute-rgt-out |
Total 43.3b remaining (32.8%)
| 10.5b | 20.3% | Toniolo and Linder, Equation (13) |
| 7.4b | 17.9% | Henrywood and Agarwal, Equation (13) |
| 6.4b | 49.5% | Henrywood and Agarwal, Equation (3) |
| 5.8b | 75.2% | Toniolo and Linder, Equation (7) |
| 4.4b | 0% | Henrywood and Agarwal, Equation (12) |