13337 calls:
| 2.0s | (/ (* (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d))) (/ (* (* (* M D) (* M D)) (* M D)) (* (* (* 2 d) (* 2 d)) (* 2 d)))) (* (* (/ l h) (/ l h)) (/ l h))) |
| 2.0s | (/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (* t (* k (tan k)))) (* (/ (sin k) l) (* t (* k (tan k))))) (* (/ (sin k) l) (* t (* k (tan k)))))) |
| 1.8s | (/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (/ (sin k) l)) (/ (sin k) l)) (* (* (* (* t k) (tan k)) (* (* t k) (tan k))) (* (* t k) (tan k))))) |
| 1.8s | (/ (* (* (* (/ 2 k) l) (* (/ 2 k) l)) (* (/ 2 k) l)) (* (* (* (/ (sin k) l) (* (* t k) (tan k))) (* (/ (sin k) l) (* (* t k) (tan k)))) (* (/ (sin k) l) (* (* t k) (tan k))))) |
| 1.7s | (* (/ (* (* (* (/ l t) (/ 2 k)) (* (/ l t) (/ 2 k))) (* (/ l t) (/ 2 k))) (* (* (/ (/ k 1) (/ l t)) (/ (/ k 1) (/ l t))) (/ (/ k 1) (/ l t)))) (* (* (/ t (* (sin k) (tan k))) (/ t (* (sin k) (tan k)))) (/ t (* (sin k) (tan k))))) |
| 55× | intervals |
| 59.5s | 241818× | body | 80 | valid |
| 42.0s | 21914× | body | 1280 | valid |
| 41.6s | 159551× | body | 80 | nan |
| 22.0s | 16574× | body | 640 | valid |
| 19.7s | 8710× | body | 10240 | exit |
| 18.0s | 7255× | body | 2560 | valid |
| 14.0s | 3419× | body | 5120 | valid |
| 8.3s | 8043× | body | 320 | valid |
| 4.9s | 8363× | body | 160 | valid |
| 646.0ms | 600× | body | 1280 | nan |
| 476.0ms | 615× | body | 640 | nan |
| 198.0ms | 340× | body | 320 | nan |
| 65.0ms | 180× | body | 160 | nan |
402 calls:
| 1.2s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.0s | (* (* (/ (cbrt (/ 2 (sin k))) t) l) (/ (/ (cbrt (/ 2 (sin k))) (/ (tan k) (/ l t))) (fma (/ k t) (/ k t) 2))) |
| 998.0ms | (sqrt (* (* (* (* 2 n) U) 1) (- t (fma (/ l Om) (* l 2) (- (* (/ U (/ Om l)) (/ n (/ Om l))) (* (/ U* (/ Om l)) (/ n (/ Om l)))))))) |
| 992.0ms | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 920.0ms | (* (* (* (fabs (/ (cbrt (/ -1 h)) (cbrt (/ -1 d)))) (sqrt (/ (cbrt (/ -1 h)) (cbrt (/ -1 d))))) (pow (/ d l) (/ 1 2))) (- 1 (* (* (* (/ 1 2) (pow (/ (* M D) (* 2 d)) 2)) h) (/ 1 l)))) |
Total 44.2b remaining (28.3%)
| 8.6b | 11.1% | Toniolo and Linder, Equation (13) |
| 8.0b | -5.5% | Henrywood and Agarwal, Equation (13) |
| 6.7b | 41.5% | Toniolo and Linder, Equation (7) |
| 4.2b | 40.8% | Henrywood and Agarwal, Equation (12) |
| 4.1b | 1.3% | Toniolo and Linder, Equation (10-) |
| 108× | rewrite-expression-head |
402 calls:
| 341.0ms | (* (hypot 1 (/ U (* 2 (* (cos (/ K 2)) J)))) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J)))) |
| 318.0ms | (cbrt (* (* (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l)) (/ (* (* (/ M 2) (/ D d)) (* (* (/ M 2) (/ D d)) h)) l))) |
| 282.0ms | (+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) |
| 275.0ms | (+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) |
| 265.0ms | (+ (sqrt (- (* (* (/ c0 h) (/ (* (/ d D) (/ d D)) w)) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) (* M M))) (* (/ c0 h) (/ (* (/ d D) (/ d D)) w))) |
| 16054× | times-frac |
| 7796× | add-sqr-sqrt |
| 7771× | *-un-lft-identity |
| 7739× | add-cube-cbrt |
| 5168× | sqrt-prod |
| 3158× | cbrt-prod |
| 1889× | div-inv |
| 1081× | associate-*r* |
| 1036× | add-exp-log |
| 903× | add-cbrt-cube |
| 898× | associate-/l* |
| 636× | pow1 |
| 465× | associate-*r/ |
| 439× | add-log-exp |
| 433× | associate-/r/ |
| 403× | expm1-log1p-u log1p-expm1-u |
| 402× | insert-posit16 |
| 380× | associate-/r* |
| 341× | associate-*l* |
| 253× | sqrt-div |
| 215× | div-exp |
| 171× | cbrt-undiv |
| 170× | prod-exp unpow-prod-up |
| 169× | flip3-- flip-- |
| 168× | associate-*l/ |
| 164× | frac-add |
| 159× | frac-times |
| 144× | cbrt-unprod |
| 138× | unpow-prod-down |
| 135× | flip-+ flip3-+ |
| 134× | cbrt-div |
| 130× | *-commutative |
| 126× | sub-neg |
| 106× | frac-2neg clear-num |
| 90× | pow-prod-down |
| 88× | prod-diff |
| 64× | distribute-rgt-in distribute-lft-in |
| 61× | fma-def |
| 56× | pow1/2 |
| 52× | associate-/l/ |
| 50× | pow1/3 |
| 49× | pow-to-exp |
| 47× | rem-sqrt-square |
| 42× | pow-unpow pow-sub |
| 40× | tan-quot |
| 38× | pow-exp |
| 23× | pow-prod-up fma-udef |
| 18× | frac-sub fma-neg |
| 17× | rec-exp pow-plus pow-pow |
| 16× | sum-log |
| 15× | pow2 |
| 14× | difference-of-sqr-1 +-commutative log-pow |
| 12× | exp-prod |
| 11× | distribute-lft-out |
| 10× | difference-of-squares associate-+r+ associate--l+ |
| 9× | log-prod |
| 8× | unpow2 |
| 7× | pow-flip expm1-udef div-sub |
| 6× | distribute-lft-out-- inv-pow cos-sum |
| 5× | associate-+l+ expm1-log1p acos-asin |
| 4× | un-div-inv diff-log |
| 3× | pow-div distribute-lft-neg-in cos-mult pow3 distribute-rgt-neg-in hypot-udef asin-acos cos-diff |
| 2× | associate-+r- distribute-rgt-out-- sin-mult distribute-neg-frac rem-cbrt-cube expm1-def |
| 1× | neg-sub0 remove-posit16 distribute-frac-neg mul0 log1p-expm1 sqrt-unprod sub-div neg-mul-1 rem-log-exp rem-square-sqrt distribute-rgt-out log1p-udef |