447 calls:
| 10.5s | (- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (* (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))) (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) |
| 10.5s | (sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))) |
| 9.5s | (- (/ (* 1.0 (* 1.0 1.0)) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))))) (/ (exp (+ (log (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) (log (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) (fma (sqrt (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x)))) 1.0 (fma 1.0 1.0 (+ (* 0.5 1.0) (/ (* 0.5 1.0) (hypot 1.0 x))))))) |
| 9.3s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))) |
| 9.3s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))) |
| 61× | intervals |
| 46.8s | 252728× | body | 80 | valid |
| 37.7s | 29502× | body | 1280 | valid |
| 27.7s | 159842× | body | 80 | nan |
| 18.9s | 19777× | body | 640 | valid |
| 18.6s | 8847× | body | 2560 | valid |
| 11.3s | 3467× | body | 5120 | valid |
| 7.1s | 10183× | body | 320 | valid |
| 4.0s | 9070× | body | 160 | valid |
| 865.0ms | 661× | body | 10240 | exit |
| 488.0ms | 604× | body | 1280 | nan |
| 266.0ms | 637× | body | 640 | nan |
| 237.0ms | 8256× | pre | 80 | true |
| 117.0ms | 212× | body | 160 | nan |
| 82.0ms | 329× | body | 320 | nan |
| 117× | rewrite-expression-head |
447 calls:
| 7.0s | (+ (sqrt (- (* (* (/ (* c0 (* (cbrt (/ d D)) (cbrt (/ d D)))) w) (/ (/ d D) (/ h (cbrt (/ d D))))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) |
| 4.1s | (* (/ c0 w) (/ (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) 2.0)) |
| 3.2s | (+ (sqrt (- (* (* (/ c0 w) (/ (/ d D) (/ h (/ d D)))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) (* M M))) (* (/ c0 w) (/ (/ d D) (/ h (/ d D))))) |
| 2.5s | (* (exp (/ (+ (+ (- EDonor Ec) Vef) mu) KbT)) (exp (/ (+ (+ (- EDonor Ec) Vef) mu) KbT))) |
| 1.8s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 44412× | add-exp-log |
| 27623× | prod-exp |
| 25916× | times-frac |
| 18694× | pow-exp |
| 18090× | div-exp |
| 13132× | *-un-lft-identity |
| 13118× | add-sqr-sqrt |
| 11878× | add-cube-cbrt |
| 7147× | pow-to-exp |
| 4774× | sqrt-prod |
| 4566× | unpow-prod-down |
| 3387× | 1-exp rec-exp |
| 2749× | associate-*r* |
| 2672× | add-cbrt-cube |
| 1573× | div-inv |
| 1413× | associate-*l* |
| 1189× | pow1 |
| 1091× | cbrt-prod |
| 901× | cbrt-unprod |
| 861× | sqr-pow |
| 723× | associate-/r/ |
| 720× | prod-diff |
| 717× | cbrt-undiv |
| 675× | associate-*r/ |
| 674× | associate-/r* |
| 579× | associate-/l* |
| 572× | distribute-lft-out |
| 495× | add-log-exp |
| 448× | log1p-expm1-u |
| 447× | expm1-log1p-u |
| 434× | tan-quot |
| 402× | pow-prod-down |
| 392× | unswap-sqr |
| 367× | exp-prod |
| 326× | pow-unpow |
| 209× | sqrt-div |
| 177× | flip3-- flip-- |
| 172× | associate-*l/ |
| 167× | distribute-lft-out-- |
| 150× | frac-times |
| 149× | sqrt-pow1 |
| 118× | *-commutative |
| 111× | frac-2neg clear-num |
| 101× | distribute-rgt-in pow-prod-up distribute-lft-in |
| 100× | pow1/2 |
| 82× | pow1/3 |
| 81× | pow-sqr |
| 80× | rem-sqrt-square |
| 76× | fma-def |
| 74× | difference-of-squares |
| 73× | fma-neg |
| 69× | associate-/l/ |
| 64× | flip-+ flip3-+ |
| 63× | swap-sqr |
| 42× | sub-neg pow-sub |
| 39× | distribute-lft-neg-in pow-pow distribute-rgt-neg-in div-sub |
| 38× | frac-add |
| 30× | neg-sub0 pow-neg |
| 25× | cos-sum |
| 21× | exp-sum |
| 20× | pow-plus |
| 19× | cbrt-div fma-udef |
| 18× | log-prod hypot-def log-pow |
| 17× | associate-+l- |
| 13× | diff-log |
| 12× | pow2 |
| 10× | sum-log pow3 |
| 8× | +-commutative unpow2 |
| 7× | distribute-rgt-out-- |
| 6× | expm1-log1p expm1-udef |
| 5× | pow-flip frac-sub cube-unmult difference-cubes inv-pow rem-log-exp |
| 4× | exp-diff log-div |
| 3× | neg-mul-1 sub-div exp-to-pow hypot-udef acos-asin |
| 2× | associate--l+ sqrt-unprod un-div-inv asin-acos rem-square-sqrt sin-mult |
| 1× | associate-+l+ quot-tan log1p-expm1 sqr-sin rem-cbrt-cube cos-diff log1p-udef |
Total 48.9b remaining (26%)
Threshold costs 4.4b (2.3%)
| 8.0b | 16% | Henrywood and Agarwal, Equation (13) |
| 7.5b | 12.8% | Henrywood and Agarwal, Equation (12) |
| 7.3b | 28.8% | Toniolo and Linder, Equation (13) |
| 6.3b | 51.4% | Henrywood and Agarwal, Equation (3) |
| 5.9b | 75.3% | Toniolo and Linder, Equation (7) |