13571 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 | (/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d))) (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2))) |
| 1.8s | (/ (* (* (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (/ (* M D) (* 2 d)) (/ (* M D) (* 2 d)))) (* (* (* (/ l h) 2) (* (/ l h) 2)) (* (/ l h) 2))) |
| 1.6s | (/ (* (* (/ 2 (* (/ k t) (/ k t))) (/ 2 (* (/ k t) (/ k t)))) (/ 2 (* (/ k t) (/ k t)))) (* (* (* (* (tan k) (tan k)) (tan k)) (* (* (/ t (* (/ l t) (/ l t))) (/ t (* (/ l t) (/ l t)))) (/ t (* (/ l t) (/ l t))))) (* (* (sin k) (sin k)) (sin k)))) |
| 1.4s | (/ (* (* (cos k) (cos k)) (cos k)) (/ (* (* (* (* k k) t) (* (* k k) t)) (* (* k k) t)) (* (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k))) (* (* (/ l (sin k)) (/ l (sin k))) (/ l (sin k)))))) |
| 55× | intervals |
| 57.0s | 227251× | body | 80 | valid |
| 46.8s | 23962× | body | 1280 | valid |
| 41.4s | 159551× | body | 80 | nan |
| 27.7s | 18248× | body | 640 | valid |
| 20.9s | 8710× | body | 10240 | exit |
| 19.2s | 7255× | body | 2560 | valid |
| 15.4s | 3419× | body | 5120 | valid |
| 8.2s | 8882× | body | 320 | valid |
| 5.3s | 8794× | body | 160 | valid |
| 659.0ms | 600× | body | 1280 | nan |
| 528.0ms | 615× | body | 640 | nan |
| 190.0ms | 340× | body | 320 | nan |
| 90.0ms | 180× | body | 160 | nan |
412 calls:
| 1.2s | (sqrt (* (* 2 n) (* U (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*)))))) |
| 1.2s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* (* n (/ l Om)) (/ l Om)) (- U U*))))) |
| 1.1s | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 955.0ms | (sqrt (* (* (* 2 n) U) (- (- t (* 2 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2)) (- U U*))))) |
| 825.0ms | (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) |
Total 50.7b remaining (31.5%)
| 11.0b | 0.5% | Henrywood and Agarwal, Equation (13) |
| 8.9b | 28.4% | Toniolo and Linder, Equation (13) |
| 8.2b | 3.3% | Maksimov and Kolovsky, Equation (3) |
| 7.4b | 70.3% | Toniolo and Linder, Equation (7) |
| 4.1b | 64.4% | Henrywood and Agarwal, Equation (3) |
| 106× | rewrite-expression-head |
412 calls:
| 610.0ms | (/ (- (pow (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4) 3) (pow (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4))) 3)) (+ (* (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4) (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4)) (+ (* (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4))) (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4)))) (* (* (+ (* (+ (* a a) a) a) (* (* b b) (- 1 (* 3 a)))) 4) (- 1 (+ (+ (pow a 4) (* (* (* a b) (* a b)) 2)) (pow b 4))))))) |
| 394.0ms | (* (sqrt (+ (* (/ U (* 2 (* (cos (/ K 2)) J))) (/ U (* 2 (* (cos (/ K 2)) J)))) 1)) (* -2 (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (* (cbrt (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (cbrt (cbrt (cos (/ K 2))))) J)))) |
| 314.0ms | (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))) |
| 288.0ms | (log (exp (+ (+ (+ (pow b 4) (pow a 4)) (* 4 (* b b))) (* (* b a) (+ (* b a) (* b a)))))) |
| 124.0ms | (sqrt (+ (* (* (* (cbrt (* (cbrt (sin kx)) (cbrt (sin kx)))) (cbrt (cbrt (sin kx)))) (sin kx)) (pow (cbrt (sin kx)) 2)) (pow (sin ky) 2))) |
| 40099× | associate-*l/ |
| 29703× | frac-add |
| 18278× | associate-*r/ |
| 15849× | flip3-- flip-- |
| 14856× | frac-times |
| 10724× | flip-+ flip3-+ |
| 10340× | times-frac |
| 8221× | associate-/r/ |
| 5618× | sqrt-prod |
| 5497× | add-sqr-sqrt |
| 5472× | *-un-lft-identity |
| 5391× | add-cube-cbrt |
| 1092× | add-exp-log |
| 949× | div-inv |
| 942× | add-cbrt-cube |
| 705× | pow1 |
| 672× | associate-*r* |
| 582× | associate-/l* |
| 471× | sqrt-div |
| 470× | add-log-exp |
| 441× | associate-/r* |
| 412× | insert-posit16 |
| 338× | associate-*l* |
| 286× | cbrt-div |
| 270× | div-exp |
| 262× | unpow-prod-up |
| 205× | sub-neg |
| 190× | unpow-prod-down |
| 168× | cbrt-undiv |
| 167× | frac-sub |
| 161× | cbrt-prod |
| 158× | prod-exp |
| 146× | cbrt-unprod |
| 145× | *-commutative |
| 109× | pow-prod-down |
| 106× | frac-2neg clear-num |
| 99× | distribute-rgt-in distribute-lft-in |
| 83× | associate-/l/ |
| 71× | pow-to-exp |
| 69× | pow1/2 |
| 55× | rem-sqrt-square |
| 48× | cube-div pow-sub |
| 45× | pow1/3 |
| 39× | pow-exp |
| 36× | rec-exp |
| 35× | pow-prod-up |
| 32× | tan-quot |
| 31× | neg-sub0 |
| 30× | pow-neg |
| 29× | associate-+r+ pow-plus |
| 25× | difference-of-squares |
| 24× | sum-log pow2 |
| 23× | associate--l+ |
| 22× | distribute-lft-out |
| 21× | distribute-lft-out-- |
| 20× | +-commutative |
| 18× | log-pow |
| 15× | pow-unpow pow-pow exp-prod |
| 14× | sub-div |
| 13× | log-prod |
| 12× | pow-flip distribute-rgt-out-- div-sub |
| 9× | unpow2 |
| 8× | associate--r+ diff-log |
| 7× | acos-asin |
| 6× | inv-pow cos-sum |
| 5× | associate-+l+ difference-of-sqr-1 sin-mult difference-cubes sqr-sin un-div-inv cube-prod |
| 4× | associate-+r- pow3 asin-acos |
| 3× | distribute-lft-neg-in distribute-rgt-neg-in cos-diff distribute-rgt-out |
| 2× | distribute-lft1-in sqrt-unprod distribute-neg-frac neg-mul-1 associate-+l- rem-square-sqrt rem-cbrt-cube associate--r- rem-log-exp distribute-rgt1-in |
| 1× | remove-posit16 distribute-frac-neg exp-sum unpow1/2 |