13116 calls:
| 2.4s | (/ (* (* (/ 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)))) |
| 2.3s | (/ (* (* (/ 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) (/ 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)))) |
| 2.1s | (/ (* (* (/ 2 (fma (/ k t) (/ k t) 2)) (/ 2 (fma (/ k t) (/ k t) 2))) (/ 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)))))) |
| 2.0s | (/ (/ (* (* 2 2) 2) (* (* (fma (/ k t) (/ k t) 2) (fma (/ k t) (/ k t) 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)))) |
| 1.9s | (* (/ (* (* (/ 1 (sqrt (fma (* v -6) v 2))) (/ 1 (sqrt (fma (* v -6) v 2)))) (/ 1 (sqrt (fma (* v -6) v 2)))) (* (* (- 1 (* v v)) (- 1 (* v v))) (* (* t t) t))) (/ (* (* (/ (fma -5 (* v v) 1) (cbrt (- 1 (* v v)))) (/ (fma -5 (* v v) 1) (cbrt (- 1 (* v v))))) (/ (fma -5 (* v v) 1) (cbrt (- 1 (* v v))))) (* (* PI PI) PI))) |
| 54× | intervals |
| 58.5s | 239338× | body | 80 | valid |
| 36.9s | 159684× | body | 80 | nan |
| 30.3s | 17567× | body | 1280 | valid |
| 19.2s | 8277× | body | 10240 | exit |
| 17.7s | 13961× | body | 640 | valid |
| 7.6s | 4981× | body | 2560 | valid |
| 6.3s | 2452× | body | 5120 | valid |
| 5.8s | 7249× | body | 320 | valid |
| 3.8s | 7923× | body | 160 | valid |
| 674.0ms | 620× | body | 1280 | nan |
| 582.0ms | 652× | body | 640 | nan |
| 184.0ms | 359× | body | 320 | nan |
| 94.0ms | 174× | body | 160 | nan |
386 calls:
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (/ (* (/ n (/ Om l)) (- U U*)) (/ Om l))))) |
| 1.7s | (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 | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (/ (/ n (/ Om l)) (/ Om l)) (- U U*))))) |
| 1.4s | (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)))) |
| 103× | rewrite-expression-head |
386 calls:
| 2.0s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 2.0s | (+ (sqrt (- (* (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) (* M M))) (/ (* (* (/ d D) (/ d D)) (/ c0 h)) w)) |
| 2.0s | (+ (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)) |
| 1.7s | (* NaChar (/ 1 (log (* E (exp (exp (/ (- Ev (- (- mu Vef) EAccept)) KbT))))))) |
| 29708× | times-frac |
| 14628× | add-sqr-sqrt |
| 14246× | *-un-lft-identity |
| 13477× | add-cube-cbrt |
| 9086× | cbrt-prod |
| 8939× | add-exp-log |
| 6415× | associate-*l* |
| 4364× | prod-exp |
| 3305× | add-cbrt-cube |
| 3101× | div-exp |
| 1550× | pow1 |
| 1201× | cbrt-undiv |
| 1063× | cbrt-unprod |
| 1022× | div-inv |
| 968× | sqrt-prod |
| 901× | associate-/l* |
| 842× | prod-diff |
| 769× | associate-*r* |
| 718× | pow-exp |
| 633× | associate-/r/ |
| 553× | 1-exp |
| 519× | sqrt-pow1 |
| 470× | pow-unpow |
| 438× | add-log-exp |
| 429× | pow-prod-down |
| 386× | expm1-log1p-u insert-posit16 log1p-expm1-u |
| 377× | difference-of-squares |
| 354× | associate-/r* |
| 329× | associate-*r/ |
| 310× | pow-prod-up |
| 276× | pow1/2 |
| 266× | associate-*l/ |
| 263× | rec-exp |
| 245× | unpow-prod-down |
| 235× | unswap-sqr |
| 224× | distribute-lft-out-- |
| 214× | frac-times |
| 195× | pow-to-exp |
| 178× | distribute-rgt-in distribute-lft-in |
| 152× | distribute-rgt-neg-in |
| 150× | distribute-lft-neg-in |
| 142× | pow-sqr |
| 138× | distribute-lft-out *-commutative |
| 123× | flip3-- flip-- |
| 89× | fma-neg |
| 88× | sqrt-div |
| 84× | frac-2neg clear-num swap-sqr |
| 69× | cos-sum |
| 64× | sqr-pow |
| 58× | pow1/3 |
| 57× | pow-plus |
| 49× | fma-def |
| 47× | sub-neg |
| 46× | cbrt-div |
| 45× | fma-udef |
| 44× | pow-pow rem-sqrt-square |
| 42× | frac-sub associate--l+ |
| 39× | pow2 |
| 36× | tan-quot |
| 30× | flip-+ flip3-+ |
| 28× | associate-/l/ |
| 19× | div-sub |
| 18× | pow-flip neg-mul-1 unpow2 |
| 14× | sum-log diff-log |
| 12× | associate--r+ inv-pow |
| 10× | +-commutative |
| 9× | frac-add |
| 8× | un-div-inv |
| 7× | pow-sub |
| 6× | exp-sum sqrt-unprod distribute-neg-frac log-pow |
| 4× | neg-sub0 pow3 |
| 3× | distribute-frac-neg hypot-udef distribute-rgt-out-- acos-asin cos-diff |
| 2× | associate-+l+ associate-+r- neg-log rem-square-sqrt rem-cbrt-cube sin-mult |
| 1× | sqrt-undiv mul0 sub-div associate--l- sqr-sin asin-acos associate--r- e-exp-1 distribute-rgt-out |
Total 45.9b remaining (33.8%)
| 9.4b | 12.8% | Toniolo and Linder, Equation (13) |
| 9.1b | 33.6% | Henrywood and Agarwal, Equation (3) |
| 6.3b | 6.8% | Henrywood and Agarwal, Equation (12) |
| 6.2b | 16.1% | Henrywood and Agarwal, Equation (13) |
| 5.5b | 76.4% | Toniolo and Linder, Equation (7) |