449 calls:
| 4.7s | (sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (* (cbrt (* (* 2.0 n) U)) (cbrt (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))) |
| 4.6s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 4.6s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 4.5s | (sqrt (* (* (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))) (cbrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (* l (/ l Om)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))))) |
| 1.6s | (- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (/ (+ (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (- (+ (* 1.0 1.0) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))) |
| 61× | intervals |
| 16.3s | 256489× | body | 80 | valid |
| 14.9s | 26553× | body | 1280 | valid |
| 10.0s | 161074× | body | 80 | nan |
| 8.6s | 8643× | body | 2560 | valid |
| 6.8s | 17447× | body | 640 | valid |
| 5.1s | 3352× | body | 5120 | valid |
| 2.1s | 8606× | body | 320 | valid |
| 1.2s | 8248× | body | 160 | valid |
| 584.0ms | 10981× | body | 80 | overflowed |
| 530.0ms | 576× | body | 10240 | exit |
| 167.0ms | 638× | body | 1280 | nan |
| 120.0ms | 8256× | pre | 80 | true |
| 119.0ms | 608× | body | 640 | nan |
| 48.0ms | 334× | body | 320 | nan |
| 19.0ms | 195× | body | 160 | nan |
| 116× | rewrite-expression-head |
449 calls:
| 1.3s | (* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l))) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) |
| 1.2s | (* (* (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (* (cbrt l) (cbrt l))) (* (/ (pow (* (cbrt t) (cbrt t)) (/ 3.0 2)) (cbrt l)) (* (/ (pow (cbrt t) 3.0) l) (sin k)))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) |
| 1.0s | (- (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)) 1.0) |
| 428.0ms | (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (* (/ (pow (cbrt t) 3.0) l) (sin k))) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0)) |
| 323.0ms | (* (* (* (pow (/ 1 (* (cbrt h) (cbrt h))) (/ 1.0 2.0)) (pow (/ d (cbrt h)) (/ 1.0 2.0))) (* (pow (/ (* (cbrt d) (cbrt d)) (* (cbrt l) (cbrt l))) (/ 1.0 2.0)) (pow (/ (cbrt d) (cbrt l)) (/ 1.0 2.0)))) (- 1.0 (/ (* (* (/ 1.0 2.0) (pow (/ (* M D) (* 2.0 d)) 2.0)) h) l))) |
| 43614× | add-exp-log |
| 29911× | prod-exp |
| 15660× | pow-exp |
| 13473× | div-exp |
| 7286× | pow-to-exp |
| 6062× | times-frac |
| 5551× | *-un-lft-identity |
| 5245× | add-sqr-sqrt |
| 4155× | add-cube-cbrt |
| 3907× | associate-*r/ |
| 3418× | sqrt-prod |
| 2761× | add-cbrt-cube |
| 2234× | cbrt-div |
| 1622× | flip3-- flip-- |
| 1594× | frac-times |
| 1398× | pow1 |
| 1235× | cbrt-unprod |
| 1233× | frac-sub |
| 1173× | associate-*r* |
| 1151× | associate-*l* |
| 1141× | sqrt-div |
| 1067× | 1-exp |
| 1061× | rec-exp |
| 945× | unpow-prod-down |
| 640× | cbrt-prod |
| 610× | associate-*l/ |
| 539× | add-log-exp |
| 530× | cbrt-undiv |
| 527× | associate-/l* |
| 517× | pow-unpow |
| 490× | distribute-lft-out |
| 430× | pow-prod-down |
| 422× | flip-+ flip3-+ |
| 390× | associate-/r* |
| 364× | distribute-lft-out-- |
| 332× | unswap-sqr |
| 304× | distribute-rgt-neg-in |
| 282× | div-inv |
| 263× | sqr-pow |
| 222× | associate-/r/ |
| 220× | distribute-lft-neg-in |
| 179× | difference-of-squares |
| 176× | frac-add |
| 174× | sqrt-pow1 |
| 148× | *-commutative |
| 111× | tan-quot |
| 95× | clear-num frac-2neg |
| 94× | pow1/2 pow1/3 |
| 89× | cube-prod |
| 77× | pow-prod-up |
| 64× | unpow2 |
| 63× | rem-sqrt-square |
| 58× | pow-pow |
| 57× | distribute-rgt-in distribute-lft-in |
| 56× | associate-/l/ |
| 48× | div-sub |
| 47× | exp-prod |
| 46× | sub-neg |
| 43× | pow-sqr |
| 35× | pow-plus |
| 34× | sum-log |
| 29× | neg-sub0 |
| 28× | +-commutative neg-mul-1 |
| 26× | pow-sub |
| 23× | swap-sqr |
| 22× | pow2 |
| 19× | pow-flip |
| 17× | pow-neg |
| 16× | log-pow |
| 14× | associate--l+ log-prod |
| 13× | exp-diff |
| 12× | distribute-neg-frac |
| 11× | diff-log sum-cubes |
| 10× | log-div |
| 9× | unpow3 cube-mult |
| 8× | pow-div associate-+r+ |
| 7× | inv-pow associate-+r- unsub-neg |
| 6× | cos-sum distribute-frac-neg |
| 5× | rem-cube-cbrt un-div-inv exp-sum |
| 4× | cube-div distribute-rgt-out-- |
| 3× | rem-exp-log cos-diff acos-asin rem-log-exp |
| 2× | sqrt-pow2 sqrt-unprod exp-to-pow pow3 sub-div rem-square-sqrt rem-cbrt-cube |
| 1× | sqrt-undiv associate-+l+ asin-acos mul0 |
| 176× | egg-herbie |
Total 51.7b remaining (22.7%)
Threshold costs 5.3b (2.3%)
| 11.3b | -6.5% | Toniolo and Linder, Equation (13) |
| 7.9b | 42.4% | Henrywood and Agarwal, Equation (3) |
| 7.8b | -19.8% | Henrywood and Agarwal, Equation (12) |
| 7.4b | 5.2% | Toniolo and Linder, Equation (10+) |
| 6.5b | 72.5% | Toniolo and Linder, Equation (7) |