13623 calls:
| 3.9s | (/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d 2) (* d 2)) (* d 2)))) (* (* 2 2) 2)) (* (* l l) l)) |
| 3.0s | (* (/ (* (* U U) U) (* (* (* 2 (* (cos (/ K 2)) J)) (* 2 (* (cos (/ K 2)) J))) (* 2 (* (cos (/ K 2)) J)))) (/ (* (* U U) U) (* (* (* 2 2) 2) (* (* (* (cos (/ K 2)) J) (* (cos (/ K 2)) J)) (* (cos (/ K 2)) J))))) |
| 2.9s | (/ (/ (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* d d) d) (* (* 2 2) 2)))) (* (* 2 2) 2)) (* (* l l) l)) |
| 2.9s | (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 2) 2) (* (* d d) d)))) (/ (* (* h h) h) (* (* l l) l))) |
| 2.5s | (* (* (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M M) M) (* (* D D) D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ h l) (/ h l)) (/ h l))) |
| 54× | intervals |
| 56.8s | 239188× | body | 80 | valid |
| 42.1s | 159760× | body | 80 | nan |
| 31.8s | 17516× | body | 1280 | valid |
| 20.9s | 8469× | body | 10240 | exit |
| 16.8s | 13976× | body | 640 | valid |
| 8.0s | 4991× | body | 2560 | valid |
| 6.5s | 7318× | body | 320 | valid |
| 5.7s | 2363× | body | 5120 | valid |
| 4.1s | 8068× | body | 160 | valid |
| 679.0ms | 651× | body | 640 | nan |
| 663.0ms | 609× | body | 1280 | nan |
| 614.0ms | 341× | body | 320 | nan |
| 113.0ms | 209× | body | 160 | nan |
393 calls:
| 1.7s | (sqrt (* (* (* (* 2 n) U) 1) (- t (* (/ l Om) (- (* l 2) (- (* (- U U*) (* (/ l Om) n)))))))) |
| 1.7s | (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) |
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.6s | (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) |
| 1.5s | (* (* (* (fabs (/ (cbrt d) (cbrt h))) (pow (/ (cbrt d) (cbrt h)) (/ 1 2))) (* (fabs (/ (cbrt d) (cbrt l))) (pow (/ (cbrt d) (cbrt l)) (/ 1 2)))) (- 1 (pow (* (/ (/ (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) 2) l) h) 1))) |
| 102× | rewrite-expression-head |
393 calls:
| 5.0s | (* (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) (cbrt J)) |
| 1.3s | (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) (* (cbrt J) (cbrt J))) |
| 1.3s | (/ NdChar (+ (exp (/ (- (- Ec (+ (+ Vef mu) EDonor))) KbT)) 1)) |
| 1.2s | (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J) |
| 1.2s | (* (* (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) -2) (cos (/ K 2))) J) |
| 26539× | times-frac |
| 12531× | add-sqr-sqrt |
| 12355× | *-un-lft-identity |
| 11542× | add-cube-cbrt |
| 6058× | add-exp-log |
| 4399× | add-cbrt-cube |
| 2844× | associate-*r* |
| 2437× | prod-exp |
| 2044× | div-exp |
| 1682× | sqrt-prod |
| 1575× | cbrt-undiv |
| 1522× | pow1 |
| 1506× | cbrt-unprod |
| 1446× | sqrt-div |
| 1359× | associate-/r/ |
| 1324× | frac-times |
| 1265× | div-inv |
| 951× | associate-*l* |
| 869× | associate-/l* |
| 856× | associate-*r/ |
| 756× | associate-*l/ |
| 653× | flip3-- flip-- |
| 619× | associate-/r* |
| 539× | pow-prod-down |
| 537× | flip-+ flip3-+ |
| 445× | add-log-exp |
| 393× | insert-posit16 |
| 306× | pow-unpow |
| 298× | pow-exp |
| 276× | unswap-sqr |
| 250× | cbrt-prod |
| 195× | unpow-prod-down |
| 194× | distribute-lft-out-- |
| 193× | difference-of-squares |
| 185× | sqrt-pow1 |
| 176× | *-commutative |
| 168× | distribute-lft-out |
| 153× | swap-sqr |
| 149× | frac-add |
| 135× | pow-to-exp |
| 109× | distribute-rgt-neg-in |
| 108× | pow1/2 tan-quot |
| 104× | distribute-rgt-out-- 1-exp |
| 101× | distribute-lft-neg-in |
| 83× | rec-exp |
| 82× | frac-2neg clear-num |
| 77× | pow-prod-up |
| 76× | sqr-pow |
| 61× | sin-mult |
| 58× | cbrt-div |
| 57× | distribute-rgt-in distribute-lft-in |
| 55× | rem-sqrt-square |
| 54× | sub-neg |
| 43× | exp-prod |
| 39× | associate-/l/ |
| 34× | pow-sqr |
| 32× | log-prod pow-plus |
| 29× | log-pow |
| 27× | pow-pow |
| 22× | pow1/3 div-sub |
| 20× | distribute-neg-frac |
| 19× | pow2 |
| 17× | sum-log |
| 16× | cos-sum |
| 15× | +-commutative |
| 12× | exp-sum |
| 11× | frac-sub neg-mul-1 |
| 10× | exp-diff cube-prod log-div |
| 9× | pow-flip pow-sub |
| 8× | associate-+l+ difference-of-sqr-1 cos-diff diff-log |
| 7× | sqr-sin inv-pow |
| 6× | associate-+r+ associate--l+ rem-log-exp asin-acos cube-div |
| 4× | associate-+r- cube-unmult rem-exp-log acos-asin |
| 2× | distribute-lft1-in sqrt-unprod sub-div exp-to-pow unpow2 rem-square-sqrt un-div-inv distribute-rgt-out |
| 1× | neg-sub0 sqrt-undiv distribute-frac-neg pow3 unpow3 sqrt-pow2 cube-mult associate--r- |
Total 45.8b remaining (27.7%)
| 8.5b | 39.4% | Henrywood and Agarwal, Equation (3) |
| 8.5b | 9.5% | Toniolo and Linder, Equation (13) |
| 7.3b | 13.1% | Maksimov and Kolovsky, Equation (3) |
| 6.1b | -23.5% | Henrywood and Agarwal, Equation (12) |
| 5.8b | 75.7% | Toniolo and Linder, Equation (7) |