| 61× | intervals |
| 44.7s | 253614× | body | 80 | valid |
| 36.1s | 29575× | body | 1280 | valid |
| 27.4s | 160606× | body | 80 | nan |
| 18.9s | 20413× | body | 640 | valid |
| 16.4s | 8910× | body | 2560 | valid |
| 8.5s | 3411× | body | 5120 | valid |
| 7.2s | 10021× | body | 320 | valid |
| 2.8s | 8980× | body | 160 | valid |
| 1.1s | 768× | body | 10240 | exit |
| 821.0ms | 621× | body | 1280 | nan |
| 780.0ms | 650× | body | 640 | nan |
| 203.0ms | 8256× | pre | 80 | true |
| 110.0ms | 189× | body | 160 | nan |
| 102.0ms | 340× | body | 320 | nan |
430 calls:
| 10.5s | (sqrt (+ (* U (* (* 2 n) (+ t (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) -2)))) (* U (* (* 2 n) (- (fma -2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) (* (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)) 2)) (* (/ (- U U*) (/ Om l)) (/ n (/ Om l)))))))) |
| 2.0s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (/ n (* (/ Om l) (/ Om l))) (- U U*))))) |
| 1.8s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* (/ l (cbrt Om)) (/ l (cbrt Om))) (cbrt Om)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.5s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 1.5s | (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) |
| 115× | rewrite-expression-head |
430 calls:
| 19.6s | (* (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (sin k))) |
| 2.8s | (* (* (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (/ k (/ l 1)))) (/ (/ (cbrt (/ 2 t)) (cbrt (tan k))) (sin k))) |
| 2.5s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 2.2s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 2.1s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 150809× | times-frac |
| 74226× | add-sqr-sqrt |
| 72250× | *-un-lft-identity |
| 71459× | add-cube-cbrt |
| 29977× | cbrt-prod |
| 26284× | unpow-prod-up |
| 25934× | prod-diff |
| 10356× | sqrt-prod |
| 6804× | add-exp-log |
| 6360× | div-inv |
| 5382× | associate-*l* |
| 5088× | add-cbrt-cube |
| 3419× | div-exp |
| 2550× | cbrt-undiv |
| 2530× | unpow-prod-down |
| 2238× | pow1 |
| 1844× | prod-exp |
| 1523× | cbrt-unprod |
| 1319× | associate-*r* |
| 1168× | associate-/l* |
| 1092× | associate-/r* |
| 1027× | sqr-pow |
| 887× | associate-/r/ |
| 688× | sub-neg |
| 574× | pow-prod-down |
| 510× | unswap-sqr |
| 501× | add-log-exp |
| 471× | pow-prod-up |
| 431× | log1p-expm1-u |
| 430× | expm1-log1p-u insert-posit16 |
| 263× | tan-quot |
| 242× | cbrt-div distribute-lft-out-- |
| 231× | difference-of-squares |
| 222× | pow-sqr |
| 193× | pow-plus |
| 182× | associate-*r/ |
| 156× | distribute-rgt-neg-in |
| 155× | 1-exp |
| 153× | distribute-lft-out |
| 150× | distribute-lft-neg-in |
| 149× | distribute-rgt-in distribute-lft-in |
| 137× | pow2 |
| 128× | *-commutative |
| 126× | sqrt-div fma-neg |
| 122× | pow1/3 |
| 118× | swap-sqr |
| 114× | flip3-- flip-- |
| 110× | pow-unpow |
| 109× | frac-2neg clear-num |
| 97× | associate-*l/ |
| 86× | sqrt-pow1 |
| 85× | pow-exp |
| 84× | frac-times |
| 70× | rem-sqrt-square |
| 69× | pow1/2 |
| 62× | pow-to-exp |
| 59× | associate-/l/ |
| 58× | pow-sub |
| 52× | exp-prod |
| 49× | log-pow |
| 41× | log-prod |
| 39× | frac-sub fma-udef |
| 35× | associate--r+ |
| 34× | associate--l+ |
| 32× | fma-def frac-add |
| 30× | flip-+ flip3-+ diff-log |
| 28× | rec-exp unpow2 |
| 24× | cos-sum |
| 22× | pow-pow |
| 18× | neg-mul-1 |
| 11× | div-sub |
| 10× | pow-flip |
| 8× | exp-sum pow3 inv-pow |
| 7× | rem-log-exp |
| 6× | sum-log neg-log +-commutative |
| 4× | hypot-udef |
| 3× | neg-sub0 cube-unmult associate--l- un-div-inv exp-to-pow distribute-rgt-out-- asin-acos rem-exp-log acos-asin associate--r- |
| 2× | remove-posit16 sqrt-undiv unpow1/2 sqrt-unprod sub-div sqr-sin hypot-def rem-cbrt-cube sin-mult |
| 1× | expm1-log1p expm1-udef exp-diff log1p-expm1 sqrt-pow2 rem-square-sqrt cos-diff e-exp-1 log1p-udef |
Total 54.6b remaining (32.9%)
Threshold costs 5.6b (3.4%)
| 10.3b | 23% | Toniolo and Linder, Equation (13) |
| 8.8b | -2.2% | Henrywood and Agarwal, Equation (13) |
| 6.3b | -4.8% | Given's Rotation SVD example |
| 5.3b | 77.2% | Toniolo and Linder, Equation (7) |
| 4.2b | 0% | Maksimov and Kolovsky, Equation (3) |