| 61× | intervals |
| 26.7s | 253023× | body | 80 | valid |
| 17.9s | 29752× | body | 1280 | valid |
| 16.7s | 161453× | body | 80 | nan |
| 9.4s | 8802× | body | 2560 | valid |
| 8.1s | 20281× | body | 640 | valid |
| 5.9s | 3366× | body | 5120 | valid |
| 2.8s | 9733× | body | 320 | valid |
| 1.6s | 9019× | body | 160 | valid |
| 432.0ms | 680× | body | 10240 | exit |
| 189.0ms | 646× | body | 1280 | nan |
| 180.0ms | 8256× | pre | 80 | overflowed |
| 151.0ms | 625× | body | 640 | nan |
| 60.0ms | 324× | body | 320 | nan |
| 28.0ms | 195× | body | 160 | nan |
439 calls:
| 5.0s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) |
| 4.8s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 4.8s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) |
| 4.7s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 1.4s | (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) |
| 115× | rewrite-expression-head |
439 calls:
| 4.9s | (* (* (* (* (* (/ (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)) |
| 1.5s | (* (* (* (* (/ (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)) |
| 1.5s | (* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (/ (cos k) (/ (/ (pow (cbrt (sin k)) 4) l) l)) (pow (cbrt (sin k)) 2))) |
| 1.2s | (* (* (* (* (/ (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)) |
| 1.1s | (* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (* (pow (/ (* (cbrt d) (cbrt d)) 1) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt h)) (/ 1.0 2.0)))) (* (pow (/ 1 (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ d (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ h l)))) |
| 107100× | add-exp-log |
| 80668× | prod-exp |
| 44196× | pow-exp |
| 32647× | div-exp |
| 31011× | times-frac |
| 15015× | add-sqr-sqrt |
| 15012× | pow-to-exp |
| 14258× | *-un-lft-identity |
| 13551× | add-cube-cbrt |
| 8813× | 1-exp |
| 8649× | unpow-prod-down |
| 6149× | rec-exp |
| 4542× | associate-*r* |
| 4219× | cbrt-prod |
| 2892× | add-cbrt-cube |
| 1638× | sqr-pow |
| 1422× | sqrt-prod |
| 1376× | pow1 |
| 1318× | cbrt-unprod |
| 964× | associate-*l/ |
| 784× | unpow2 |
| 762× | associate-*l* |
| 608× | associate-*r/ |
| 603× | add-log-exp |
| 600× | associate-/l* |
| 542× | frac-times |
| 537× | cbrt-undiv |
| 515× | div-inv |
| 512× | pow-unpow |
| 447× | pow-prod-down |
| 429× | unswap-sqr |
| 362× | flip-+ flip3-+ |
| 298× | sqrt-div |
| 295× | flip3-- flip-- |
| 261× | associate-/r* |
| 232× | exp-prod |
| 213× | distribute-lft-out-- |
| 207× | associate-/r/ |
| 201× | distribute-lft-out |
| 176× | cbrt-div |
| 172× | frac-sub |
| 144× | difference-of-squares |
| 143× | *-commutative distribute-rgt-neg-in |
| 113× | tan-quot |
| 102× | distribute-lft-neg-in |
| 99× | sqrt-pow1 |
| 96× | associate-/l/ |
| 87× | rem-sqrt-square |
| 84× | clear-num frac-2neg |
| 80× | distribute-rgt-in pow1/2 distribute-lft-in |
| 69× | sub-neg |
| 66× | frac-add |
| 59× | pow-pow |
| 51× | swap-sqr |
| 50× | pow1/3 |
| 49× | pow-prod-up |
| 46× | diff-log |
| 45× | sum-log |
| 44× | log-prod |
| 38× | div-sub |
| 33× | pow-sqr |
| 32× | pow-sub |
| 27× | +-commutative |
| 25× | associate-+r+ |
| 24× | exp-diff |
| 23× | pow-plus associate--l+ |
| 21× | associate-+l+ neg-sub0 |
| 18× | log-div |
| 17× | pow2 |
| 16× | rem-exp-log |
| 14× | exp-sum pow-neg |
| 12× | neg-mul-1 |
| 10× | un-div-inv |
| 9× | log-pow pow-flip unpow-prod-up associate-+r- neg-log |
| 7× | inv-pow unsub-neg associate--r- |
| 5× | e-exp-1 |
| 4× | distribute-neg-in associate--r+ |
| 3× | associate--l- exp-neg distribute-frac-neg acos-asin |
| 2× | distribute-rgt-out asin-acos cos-sum rem-log-exp |
| 1× | sqrt-undiv distribute-lft1-in sqrt-unprod cos-diff unpow1/2 rem-square-sqrt sub-div mul0 |
| 175× | egg-herbie |
Total 44.4b remaining (20.9%)
Threshold costs 5.2b (2.4%)
| 8.0b | 10% | Toniolo and Linder, Equation (13) |
| 7.8b | 67.5% | Toniolo and Linder, Equation (7) |
| 5.5b | 19.6% | Toniolo and Linder, Equation (10+) |
| 4.6b | 12.3% | Henrywood and Agarwal, Equation (12) |
| 4.0b | 67.1% | Henrywood and Agarwal, Equation (3) |