23251 calls:
| 2.6s | (/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (/ (* (* (* (* t t) t) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (/ (* (* t t) t) (/ (* (* l l) l) (* (* (sin k) (sin k)) (sin k))))) (* (* (cos k) (cos k)) (cos k)))) |
| 2.3s | (* (* (* h h) h) (* (* (/ 1 l) (/ 1 l)) (* (/ 1 l) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))))) |
| 2.2s | (* (* (* h h) h) (* (/ (* (* 1 1) 1) (* (* l l) l)) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))))) |
| 1.9s | (/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 2 (fma (/ k t) (/ k t) 2))) (* (* (* (* (sin k) (tan k)) (* (sin k) (tan k))) (* (sin k) (tan k))) (/ (* (* t t) t) (* (/ (* (* l l) l) (* (* t t) t)) (/ (* (* l l) l) (* (* t t) t)))))) |
| 1.9s | (sqrt (+ (* 1 1) (+ (* (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))) (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d)))) (* 1 (* (* h (* (* (cbrt (/ 1 l)) (cbrt (/ 1 l))) (* (cbrt (/ 1 l)) (/ (* M D) (* 2 d))))) (/ (* M D) (* 2 d))))))) |
| 57× | intervals |
| 56.2s | 239252× | body | 80 | valid |
| 39.6s | 144380× | body | 80 | nan |
| 35.1s | 21278× | body | 1280 | valid |
| 19.7s | 8373× | body | 10240 | exit |
| 18.9s | 14802× | body | 640 | valid |
| 8.5s | 5892× | body | 2560 | valid |
| 6.2s | 2443× | body | 5120 | valid |
| 5.9s | 7738× | body | 320 | valid |
| 4.6s | 8248× | body | 160 | valid |
| 673.0ms | 565× | body | 1280 | nan |
| 596.0ms | 616× | body | 640 | nan |
| 454.0ms | 8256× | pre | 80 | true |
| 263.0ms | 385× | body | 320 | nan |
| 78.0ms | 200× | body | 160 | nan |
410 calls:
| 2.0s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))) |
| 1.9s | (sqrt (* (* (cbrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))) (cbrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*)))))) (cbrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))))) |
| 1.6s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.6s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- 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)))))) |
| 110× | rewrite-expression-head |
410 calls:
| 1.7s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 1.7s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (/ d D) (* (/ d D) (/ c0 h))) w)) |
| 1.0s | (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1) |
| 923.0ms | (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) |
| 852.0ms | (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) |
| 47459× | times-frac |
| 22115× | add-sqr-sqrt |
| 21776× | *-un-lft-identity |
| 20765× | add-cube-cbrt |
| 8833× | associate-*r/ |
| 6298× | frac-times cbrt-div |
| 5203× | flip3-- flip-- |
| 5139× | frac-sub |
| 4478× | add-exp-log |
| 4142× | associate-*r* |
| 3842× | cbrt-prod |
| 3773× | add-cbrt-cube |
| 2340× | sqrt-div |
| 2209× | div-inv |
| 2182× | sqrt-prod |
| 1746× | div-exp |
| 1735× | pow1 |
| 1659× | associate-*l/ |
| 1603× | cbrt-undiv |
| 1406× | prod-diff |
| 1370× | prod-exp |
| 1251× | associate-/l* |
| 1219× | associate-*l* |
| 1173× | cbrt-unprod |
| 840× | associate-/r* |
| 744× | associate-/r/ |
| 714× | difference-of-squares |
| 528× | pow-prod-down |
| 477× | unpow-prod-down |
| 470× | add-log-exp |
| 414× | expm1-log1p-u |
| 410× | log1p-expm1-u insert-posit16 |
| 298× | pow-prod-up |
| 237× | distribute-lft-out-- |
| 231× | pow1/3 |
| 230× | pow-unpow |
| 225× | unswap-sqr |
| 219× | sqr-pow |
| 194× | sqrt-pow1 |
| 192× | distribute-rgt-neg-in |
| 191× | distribute-lft-out |
| 188× | distribute-lft-neg-in |
| 157× | pow-sqr |
| 131× | *-commutative |
| 127× | swap-sqr |
| 115× | pow1/2 fma-neg |
| 113× | pow-plus |
| 107× | frac-2neg clear-num |
| 93× | distribute-rgt-in distribute-lft-in |
| 75× | pow-exp |
| 69× | pow2 |
| 64× | rem-sqrt-square |
| 48× | pow-to-exp |
| 47× | fma-udef |
| 46× | 1-exp rec-exp |
| 42× | associate-/l/ |
| 40× | sub-neg |
| 37× | fma-def |
| 34× | tan-quot |
| 33× | associate--l+ |
| 32× | flip-+ unpow2 flip3-+ |
| 25× | cos-sum |
| 24× | diff-log |
| 23× | pow-pow |
| 22× | associate--r+ |
| 21× | div-sub |
| 20× | neg-mul-1 |
| 19× | log-pow exp-prod |
| 15× | hypot-udef |
| 14× | hypot-def |
| 12× | pow-flip sqrt-unprod |
| 10× | log-prod inv-pow |
| 9× | pow-sub |
| 8× | sum-log |
| 7× | +-commutative |
| 5× | log1p-udef |
| 4× | neg-sub0 expm1-udef log1p-expm1 neg-log distribute-neg-frac frac-add |
| 3× | expm1-log1p associate-+r- rem-log-exp distribute-rgt-out-- asin-acos rem-square-sqrt sin-mult |
| 2× | associate-+r+ distribute-frac-neg cube-unmult associate--l- rem-exp-log acos-asin associate--r- |
| 1× | sqrt-undiv mul0 exp-sum pow3 difference-of-sqr-1 sub-div sqr-sin cos-diff expm1-def |
Total 34.5b remaining (27.4%)
Threshold costs 3.8b (3%)
| 7.9b | 47.2% | Henrywood and Agarwal, Equation (3) |
| 6.9b | 14.7% | Henrywood and Agarwal, Equation (13) |
| 5.9b | 74.8% | Toniolo and Linder, Equation (7) |
| 4.5b | -11.9% | Maksimov and Kolovsky, Equation (3) |
| 4.3b | 30.4% | Henrywood and Agarwal, Equation (12) |