| 61× | intervals |
| 1.0m | 252766× | body | 80 | valid |
| 53.4s | 29602× | body | 1280 | valid |
| 39.3s | 160249× | body | 80 | nan |
| 26.2s | 20103× | body | 640 | valid |
| 20.5s | 8671× | body | 2560 | valid |
| 12.3s | 3391× | body | 5120 | valid |
| 10.5s | 10122× | body | 320 | valid |
| 5.3s | 8905× | body | 160 | valid |
| 2.2s | 818× | body | 10240 | exit |
| 674.0ms | 624× | body | 1280 | nan |
| 564.0ms | 646× | body | 640 | nan |
| 554.0ms | 8256× | pre | 80 | true |
| 182.0ms | 348× | body | 320 | nan |
| 72.0ms | 205× | body | 160 | nan |
447 calls:
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (/ l Om)) (* (/ l Om) (- U U*)))))) |
| 1.7s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))) |
| 1.7s | (sqrt (- 1 (* (* (* (cbrt (/ (/ 1 (sqrt 2)) l)) (cbrt (/ (/ 1 (sqrt 2)) l))) (* (cbrt (/ (/ 1 (sqrt 2)) l)) (/ (/ (/ (* M D) d) (sqrt 2)) (/ 1 h)))) (/ (/ (* M D) d) 2)))) |
| 1.6s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.6s | (* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) |
| 118× | rewrite-expression-head |
447 calls:
| 3.0s | (cbrt (* (* (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1) (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1)) (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1))) |
| 1.4s | (+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) |
| 1.2s | (* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (/ (/ (* (* (/ (* M D) (* d 2)) (/ (* M D) (* d 2))) h) l) 2))) |
| 1.1s | (* (* (* (sqrt (* (/ (cbrt d) (cbrt h)) (/ (cbrt d) (cbrt h)))) (sqrt (/ (cbrt d) (cbrt h)))) (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l))))) (- 1 (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) (/ h l)))) |
| 1.0s | (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))) |
| 199717× | times-frac |
| 97260× | *-un-lft-identity |
| 88255× | add-sqr-sqrt |
| 70004× | add-cube-cbrt |
| 24167× | sqrt-prod |
| 16147× | cbrt-prod |
| 10377× | difference-of-squares |
| 8373× | div-inv |
| 7949× | add-exp-log |
| 5923× | distribute-lft-out |
| 5296× | add-cbrt-cube |
| 5117× | associate-*l* |
| 5053× | distribute-lft-out-- |
| 3721× | div-exp |
| 2995× | prod-diff |
| 2517× | associate-/r/ |
| 2461× | prod-exp |
| 2363× | cbrt-undiv |
| 2290× | associate-*r* |
| 2227× | associate-/r* |
| 1672× | unpow-prod-up |
| 1497× | cbrt-unprod |
| 1372× | pow1 |
| 1059× | associate-/l* |
| 911× | flip-+ flip3-+ |
| 774× | sqrt-div |
| 688× | frac-times |
| 675× | unswap-sqr |
| 554× | associate-*r/ |
| 512× | add-log-exp |
| 509× | associate-*l/ |
| 507× | flip3-- flip-- |
| 506× | swap-sqr |
| 448× | expm1-log1p-u |
| 447× | log1p-expm1-u insert-posit16 |
| 435× | pow-prod-down |
| 423× | unpow-prod-down |
| 329× | 1-exp |
| 227× | distribute-rgt-in distribute-lft-in |
| 223× | pow-exp |
| 161× | sqr-pow |
| 158× | rec-exp |
| 157× | sqrt-pow1 |
| 139× | *-commutative tan-quot |
| 137× | pow-unpow |
| 136× | distribute-rgt-neg-in |
| 132× | distribute-lft-neg-in |
| 119× | frac-2neg clear-num |
| 113× | sub-neg |
| 106× | frac-sub |
| 97× | fma-neg |
| 95× | pow-to-exp |
| 93× | pow1/2 |
| 67× | associate-/l/ |
| 59× | pow1/3 |
| 54× | pow-prod-up |
| 53× | log-pow |
| 52× | cbrt-div unpow2 |
| 50× | fma-udef |
| 46× | rem-sqrt-square exp-prod |
| 42× | associate--l+ |
| 39× | fma-def |
| 36× | pow-sqr |
| 34× | pow-pow |
| 31× | log-prod |
| 27× | associate--r+ cos-sum |
| 24× | pow-plus |
| 22× | diff-log |
| 19× | pow2 |
| 13× | div-sub |
| 12× | sum-log neg-mul-1 |
| 11× | pow-flip +-commutative inv-pow |
| 10× | hypot-udef |
| 8× | hypot-def pow-sub |
| 7× | exp-sum rem-log-exp |
| 6× | frac-add |
| 5× | acos-asin |
| 4× | associate-+r+ neg-log sqrt-unprod rem-square-sqrt log-div |
| 3× | un-div-inv asin-acos rem-exp-log |
| 2× | associate-+l+ expm1-log1p neg-sub0 expm1-udef exp-diff sin-sum associate-+r- pow3 associate--l- sqr-sin associate-+l- log1p-def associate--r- sin-mult |
| 1× | cube-unmult log1p-expm1 sqrt-pow2 exp-to-pow rem-cbrt-cube cos-diff log1p-udef |
Total 46.3b remaining (25.3%)
Threshold costs 5.8b (3.2%)
| 7.7b | 17% | Toniolo and Linder, Equation (13) |
| 6.1b | 20.1% | Henrywood and Agarwal, Equation (13) |
| 5.7b | 18.2% | Henrywood and Agarwal, Equation (12) |
| 5.4b | 30.5% | Henrywood and Agarwal, Equation (3) |
| 5.2b | 78.3% | Toniolo and Linder, Equation (7) |