434 calls:
| 12.1s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U*) 1 (* U* 1))))))) 2.0))) |
| 11.8s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U*) 1 (* U* 1))))))) 2.0))) |
| 11.6s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (+ (* (pow (/ l Om) (/ 2.0 2)) (* (* (pow (/ l Om) (/ 2.0 2)) n) (- U U*))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (fma (- U*) 1 (* U* 1))))))) 2.0))) |
| 8.9s | (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))) |
| 8.6s | (/ (- (* 1.0 (* 1.0 1.0)) (* (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))) (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (fma 1.0 1.0 (fma 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) |
| 60× | intervals |
| 42.7s | 250113× | body | 80 | valid |
| 28.6s | 25455× | body | 1280 | valid |
| 27.2s | 160173× | body | 80 | nan |
| 17.3s | 17755× | body | 640 | valid |
| 9.9s | 6513× | body | 2560 | valid |
| 5.4s | 8961× | body | 320 | valid |
| 3.5s | 8657× | body | 160 | valid |
| 3.1s | 2434× | body | 5120 | valid |
| 930.0ms | 644× | body | 10240 | exit |
| 495.0ms | 176× | body | 160 | nan |
| 381.0ms | 623× | body | 1280 | nan |
| 376.0ms | 670× | body | 640 | nan |
| 268.0ms | 340× | body | 320 | nan |
| 204.0ms | 8256× | pre | 80 | true |
| 114× | rewrite-expression-head |
434 calls:
| 4.3s | (* (* (* (* (/ (/ (pow (cbrt t) 3.0) (cbrt l)) (cbrt l)) (/ (pow (cbrt t) 3.0) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) |
| 3.2s | (* (* (* (/ (/ (pow (cbrt t) 3.0) (cbrt l)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) |
| 1.9s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 1.6s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 1.6s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 460267× | times-frac |
| 182068× | add-sqr-sqrt |
| 181469× | *-un-lft-identity |
| 180895× | add-cube-cbrt |
| 151116× | unpow-prod-down |
| 134808× | cbrt-prod |
| 87192× | sqrt-prod |
| 15447× | sqr-pow |
| 15028× | add-exp-log |
| 13009× | div-inv |
| 8675× | prod-exp |
| 4551× | div-exp |
| 3724× | associate-/r/ |
| 3070× | pow-exp |
| 2674× | add-cbrt-cube |
| 2667× | tan-quot |
| 1365× | prod-diff |
| 1318× | pow-to-exp |
| 1270× | pow1 |
| 1249× | associate-/l* |
| 1068× | cbrt-unprod |
| 1063× | associate-/r* |
| 875× | associate-*r/ |
| 835× | associate-*l* |
| 785× | associate-*r* |
| 766× | cbrt-div |
| 646× | cbrt-undiv |
| 534× | associate-*l/ |
| 528× | frac-times |
| 499× | add-log-exp |
| 434× | pow-prod-down expm1-log1p-u log1p-expm1-u |
| 326× | distribute-rgt-in distribute-lft-in |
| 315× | 1-exp |
| 313× | rec-exp |
| 306× | pow-unpow |
| 262× | difference-of-squares |
| 237× | unswap-sqr |
| 221× | sqrt-div |
| 188× | flip3-- flip-- |
| 169× | distribute-lft-out-- |
| 148× | distribute-lft-out |
| 144× | *-commutative |
| 128× | exp-sum |
| 118× | flip-+ flip3-+ |
| 108× | sqrt-pow1 |
| 106× | unpow-prod-up |
| 97× | frac-2neg clear-num |
| 87× | pow1/2 |
| 84× | rem-sqrt-square |
| 69× | pow1/3 |
| 60× | fma-neg |
| 53× | swap-sqr |
| 49× | sub-neg |
| 48× | associate-/l/ frac-add |
| 47× | fma-def |
| 46× | pow-pow |
| 40× | distribute-lft-neg-in distribute-rgt-neg-in |
| 35× | associate--l+ |
| 30× | pow-sub |
| 26× | exp-prod |
| 24× | pow-prod-up |
| 23× | cos-sum |
| 21× | div-sub |
| 20× | fma-udef diff-log |
| 18× | neg-sub0 pow-neg |
| 14× | pow-sqr |
| 13× | sum-log +-commutative |
| 12× | hypot-def |
| 11× | frac-sub |
| 8× | pow-flip |
| 6× | pow2 pow-plus rem-exp-log associate-+l- |
| 5× | inv-pow un-div-inv log-pow |
| 4× | log-prod neg-mul-1 acos-asin |
| 3× | hypot-udef |
| 2× | exp-diff sqrt-unprod asin-acos rem-square-sqrt |
| 1× | expm1-log1p expm1-udef sqrt-undiv distribute-rgt-neg-out sub-div associate--l- rem-log-exp cos-diff |
Total 59.7b remaining (30.3%)
Threshold costs 3.5b (1.8%)
| 11.5b | -11.2% | Toniolo and Linder, Equation (13) |
| 8.8b | 42.2% | Henrywood and Agarwal, Equation (3) |
| 8.7b | 43.1% | Toniolo and Linder, Equation (10+) |
| 8.5b | -3.1% | Henrywood and Agarwal, Equation (12) |
| 7.1b | 10.4% | Henrywood and Agarwal, Equation (13) |