| 61× | intervals |
| 1.1m | 252107× | body | 80 | valid |
| 56.7s | 29449× | body | 1280 | valid |
| 40.1s | 158999× | body | 80 | nan |
| 27.2s | 20074× | body | 640 | valid |
| 24.2s | 8862× | body | 2560 | valid |
| 14.0s | 3447× | body | 5120 | valid |
| 10.5s | 9912× | body | 320 | valid |
| 5.2s | 8973× | body | 160 | valid |
| 1.5s | 626× | body | 10240 | exit |
| 704.0ms | 627× | body | 1280 | nan |
| 466.0ms | 638× | body | 640 | nan |
| 315.0ms | 8256× | pre | 80 | true |
| 294.0ms | 361× | body | 320 | nan |
| 65.0ms | 194× | body | 160 | nan |
427 calls:
| 2.4s | (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) |
| 1.9s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))) |
| 1.7s | (* (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (sqrt (/ (/ 1 (cbrt l)) (cbrt l))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) |
| 1.6s | (fma (/ 3 (* t (* (sqrt 2) 2))) (/ (* v v) PI) (- (/ (/ (* (* (* v v) (* v v)) 27/2) (* PI (pow (sqrt 2) 5))) t) (fma (/ 2/3 (* (sqrt 2) t)) (/ (* v v) PI) (fma (/ 2 (* t (* (sqrt 2) 2))) (/ (* (* v v) (* v v)) PI) (* (/ 31/9 (* (sqrt 2) t)) (/ (* (* v v) (* v v)) PI)))))) |
| 1.5s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))) |
| 114× | rewrite-expression-head |
427 calls:
| 2.4s | (* (* (sqrt (/ 1 (* (cbrt h) (cbrt h)))) (sqrt (/ d (cbrt h)))) (* (* (sqrt (/ d (cbrt l))) (sqrt (/ (/ 1 (cbrt l)) (cbrt l)))) (* (* 1/2 (* (/ M (/ 2 (/ D d))) (/ M (/ 2 (/ D d))))) (- (/ h l))))) |
| 1.7s | (+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) |
| 1.5s | (+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (* (/ c0 h) (/ d D)) (/ (/ d D) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) |
| 891.0ms | (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) |
| 798.0ms | (- (- (pow (- (/ (+ m n) 2) M) 2)) (posit16->real (real->posit16 (- l (fabs (- m n)))))) |
| 45235× | times-frac |
| 25517× | add-sqr-sqrt |
| 23578× | *-un-lft-identity |
| 22746× | add-cube-cbrt |
| 10551× | sqrt-prod |
| 7802× | add-exp-log |
| 6548× | prod-diff |
| 5972× | add-cbrt-cube |
| 5781× | unpow-prod-up |
| 3544× | associate-*l* |
| 3132× | cbrt-prod |
| 3081× | div-exp |
| 3007× | prod-exp |
| 2242× | cbrt-unprod |
| 2241× | cbrt-undiv |
| 2164× | pow1 |
| 1876× | div-inv |
| 1306× | associate-*r* |
| 1091× | associate-/l* |
| 863× | associate-/r* |
| 674× | associate-*r/ |
| 654× | pow-prod-down |
| 577× | frac-times |
| 550× | sqrt-div |
| 528× | unswap-sqr |
| 513× | add-log-exp |
| 500× | unpow-prod-down |
| 429× | expm1-log1p-u |
| 427× | log1p-expm1-u insert-posit16 |
| 394× | associate-*l/ |
| 355× | pow-prod-up |
| 312× | difference-of-squares |
| 226× | sqr-pow |
| 224× | pow-exp |
| 214× | distribute-rgt-neg-in |
| 210× | distribute-rgt-in distribute-lft-in |
| 208× | 1-exp |
| 207× | distribute-lft-neg-in distribute-lft-out-- associate-/r/ |
| 203× | sub-neg |
| 193× | flip3-- flip-- |
| 172× | pow-sqr |
| 144× | fma-neg |
| 138× | sqrt-pow1 |
| 136× | *-commutative |
| 133× | pow-plus |
| 129× | swap-sqr |
| 128× | pow-unpow |
| 126× | tan-quot |
| 109× | frac-sub |
| 108× | distribute-lft-out |
| 99× | pow1/2 |
| 96× | distribute-neg-in pow2 |
| 92× | frac-2neg clear-num |
| 88× | pow-to-exp |
| 86× | pow1/3 |
| 80× | rec-exp |
| 75× | rem-sqrt-square |
| 68× | distribute-neg-frac |
| 51× | associate-/l/ |
| 49× | fma-udef |
| 48× | log-prod exp-sum |
| 46× | fma-def |
| 44× | exp-prod |
| 43× | flip-+ associate--l+ flip3-+ |
| 41× | unpow2 |
| 35× | associate--r+ |
| 34× | diff-log |
| 27× | pow-pow |
| 24× | cbrt-div |
| 23× | neg-mul-1 cos-sum |
| 17× | pow-flip cube-unmult |
| 12× | frac-add pow-sub |
| 11× | sum-log +-commutative inv-pow |
| 10× | div-sub |
| 9× | hypot-def |
| 7× | neg-log un-div-inv |
| 6× | neg-sub0 |
| 4× | remove-posit16 exp-diff distribute-rgt-neg-out associate--l- |
| 3× | associate-+r- exp-neg associate-+l- acos-asin associate--r- distribute-rgt-out-- |
| 2× | associate-+l+ expm1-log1p expm1-udef associate-+r+ log1p-expm1 sqrt-unprod hypot-udef asin-acos rem-exp-log rem-square-sqrt log1p-udef |
| 1× | sqrt-undiv sub-div sqr-sin cos-diff sin-mult |
Total 52.2b remaining (28.9%)
Threshold costs 4.3b (2.4%)
| 8.4b | 9.7% | Toniolo and Linder, Equation (10+) |
| 8.4b | 13.2% | Toniolo and Linder, Equation (13) |
| 8.2b | 2.2% | Henrywood and Agarwal, Equation (12) |
| 7.6b | -1.1% | Henrywood and Agarwal, Equation (13) |
| 5.1b | 78.1% | Toniolo and Linder, Equation (7) |