429 calls:
| 4.7s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 4.5s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) |
| 4.5s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 4.3s | (sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))) |
| 1.3s | (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) |
| 61× | intervals |
| 19.0s | 253420× | body | 80 | valid |
| 18.3s | 29516× | body | 1280 | valid |
| 12.1s | 161922× | body | 80 | nan |
| 10.1s | 8746× | body | 2560 | valid |
| 8.5s | 20381× | body | 640 | valid |
| 6.7s | 3321× | body | 5120 | valid |
| 2.8s | 9886× | body | 320 | valid |
| 1.4s | 8928× | body | 160 | valid |
| 916.0ms | 944× | body | 10240 | exit |
| 192.0ms | 613× | body | 1280 | nan |
| 164.0ms | 657× | body | 640 | nan |
| 92.0ms | 8256× | pre | 80 | true |
| 71.0ms | 362× | body | 320 | nan |
| 26.0ms | 209× | body | 160 | nan |
| 115× | rewrite-expression-head |
429 calls:
| 2.3s | (/ (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) |
| 1.7s | (* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt (cbrt h)) (cbrt (cbrt h)))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt (cbrt h))) (/ 1.0 2.0)))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))) |
| 1.1s | (* (* (* (/ (pow (cbrt t) 3.0) (/ l (pow (cbrt t) 3.0))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) |
| 938.0ms | (/ NdChar (sqrt (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))) |
| 932.0ms | (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) |
| 89012× | add-exp-log |
| 66092× | prod-exp |
| 32793× | pow-exp |
| 23199× | div-exp |
| 11016× | pow-to-exp |
| 5058× | times-frac |
| 4612× | add-sqr-sqrt |
| 4324× | *-un-lft-identity |
| 3726× | add-cube-cbrt |
| 2865× | 1-exp rec-exp |
| 2709× | add-cbrt-cube |
| 2034× | associate-*r/ |
| 1773× | sqrt-prod |
| 1597× | unpow-prod-down |
| 1359× | pow1 |
| 1167× | cbrt-unprod |
| 1060× | associate-*l* |
| 1022× | cbrt-div |
| 953× | associate-*r* |
| 929× | flip3-- flip-- |
| 858× | cbrt-prod |
| 831× | frac-times |
| 641× | sqrt-div |
| 624× | frac-sub |
| 525× | cbrt-undiv |
| 485× | pow-prod-down |
| 471× | add-log-exp |
| 429× | log1p-expm1-u expm1-log1p-u |
| 407× | associate-/r* |
| 397× | associate-/l* |
| 385× | sqr-pow |
| 338× | associate-*l/ |
| 301× | prod-diff |
| 278× | pow-unpow |
| 273× | div-inv |
| 255× | unswap-sqr |
| 206× | distribute-lft-out |
| 186× | distribute-rgt-in distribute-lft-in |
| 171× | flip-+ flip3-+ |
| 145× | difference-of-squares *-commutative |
| 141× | distribute-lft-out-- |
| 128× | associate-/r/ |
| 106× | distribute-rgt-neg-in |
| 93× | clear-num frac-2neg |
| 88× | sqrt-pow1 |
| 82× | distribute-lft-neg-in |
| 77× | pow1/3 |
| 69× | cos-sum tan-quot |
| 67× | fma-def |
| 60× | pow1/2 |
| 54× | sub-neg |
| 52× | pow-pow |
| 51× | log-prod |
| 50× | rem-sqrt-square |
| 45× | associate-/l/ |
| 42× | exp-prod |
| 39× | pow-prod-up |
| 36× | swap-sqr |
| 32× | associate--l+ unpow2 |
| 28× | log-pow |
| 27× | pow-sqr div-sub |
| 26× | fma-udef |
| 22× | pow-plus associate-+r+ |
| 17× | sum-log |
| 16× | exp-diff log-div |
| 15× | +-commutative hypot-def |
| 14× | frac-add pow-sub exp-sum |
| 12× | pow2 |
| 10× | neg-mul-1 |
| 8× | un-div-inv pow-flip |
| 7× | fma-neg rem-log-exp |
| 6× | inv-pow neg-sub0 |
| 5× | unpow-prod-up diff-log |
| 4× | rem-exp-log asin-acos associate-+r- sqrt-unprod hypot-udef acos-asin distribute-neg-frac |
| 3× | cos-diff |
| 2× | pow-neg pow3 unsub-neg distribute-frac-neg |
| 1× | pow-div associate-+l+ e-exp-1 rem-square-sqrt mul0 rem-cbrt-cube |
Total 43.5b remaining (23.7%)
Threshold costs 4.9b (2.7%)
| 9.3b | 3.1% | Toniolo and Linder, Equation (13) |
| 8.3b | 42.4% | Henrywood and Agarwal, Equation (3) |
| 5.5b | 77.1% | Toniolo and Linder, Equation (7) |
| 4.2b | 44.4% | Henrywood and Agarwal, Equation (12) |
| 3.9b | 44.8% | Toniolo and Linder, Equation (10-) |
| 175× | egg-herbie |