| 61× | intervals |
| 41.0s | 252181× | body | 80 | valid |
| 39.7s | 29453× | body | 1280 | valid |
| 31.5s | 160173× | body | 80 | nan |
| 19.4s | 20296× | body | 640 | valid |
| 17.2s | 8772× | body | 2560 | valid |
| 10.9s | 3360× | body | 5120 | valid |
| 5.7s | 9995× | body | 320 | valid |
| 4.4s | 9078× | body | 160 | valid |
| 963.0ms | 644× | body | 10240 | exit |
| 351.0ms | 623× | body | 1280 | nan |
| 343.0ms | 670× | body | 640 | nan |
| 174.0ms | 8256× | pre | 80 | true |
| 132.0ms | 340× | body | 320 | nan |
| 33.0ms | 176× | body | 160 | nan |
445 calls:
| 7.6s | (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*))))) |
| 7.3s | (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*)))))) |
| 7.2s | (sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) |
| 7.2s | (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*))))) |
| 2.3s | (* (* (* 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*))))) |
| 114× | rewrite-expression-head |
445 calls:
| 3.1s | (* (* (* (* (/ (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)) |
| 2.7s | (* (* (* (/ (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)) |
| 1.3s | (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))) |
| 1.3s | (* (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0))))) (sqrt (/ (- (* (* 1.0 1.0) 1.0) (* (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5))) (+ (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5) (* 1.0 (+ (sqrt (* (+ (/ 1.0 (hypot 1.0 x)) 1.0) 0.5)) 1.0)))))) |
| 1.1s | (- (+ (* (* (/ (exp (* m (+ 0 (log k)))) (* k k)) (/ a (* k k))) 99.0) (* (/ a k) (/ (exp (* m (+ 0 (log k)))) k))) (* (/ (* 10.0 (exp (* m (+ 0 (log k))))) (* k k)) (/ a k))) |
| 20424× | add-exp-log |
| 13613× | prod-exp |
| 5197× | div-exp |
| 4652× | pow-exp |
| 3874× | add-sqr-sqrt |
| 3662× | times-frac |
| 3506× | *-un-lft-identity |
| 2941× | add-cube-cbrt |
| 2832× | add-cbrt-cube |
| 2232× | sqrt-prod |
| 2224× | pow-to-exp |
| 1325× | pow1 |
| 1300× | associate-*l* |
| 1248× | cbrt-unprod |
| 869× | associate-*l/ |
| 773× | frac-times |
| 766× | associate-*r* |
| 763× | associate-*r/ |
| 725× | sqrt-div |
| 675× | unpow-prod-down |
| 614× | 1-exp rec-exp |
| 568× | cbrt-undiv |
| 555× | add-log-exp |
| 442× | pow-prod-down |
| 359× | flip-+ flip3-+ frac-add |
| 358× | pow-unpow |
| 332× | associate-/l* |
| 310× | cbrt-prod |
| 292× | flip3-- flip-- |
| 278× | associate-/r* |
| 259× | unswap-sqr |
| 229× | div-inv |
| 216× | frac-sub |
| 196× | sqr-pow |
| 185× | distribute-lft-out |
| 166× | cbrt-div |
| 150× | *-commutative |
| 146× | difference-of-squares |
| 143× | sqrt-pow1 |
| 127× | distribute-lft-out-- |
| 125× | associate-/r/ |
| 111× | pow1/2 |
| 109× | tan-quot |
| 96× | rem-sqrt-square |
| 86× | frac-2neg clear-num |
| 75× | sub-neg |
| 71× | distribute-rgt-in distribute-lft-in |
| 61× | swap-sqr |
| 54× | pow1/3 |
| 49× | associate-/l/ |
| 45× | distribute-rgt-neg-in distribute-lft-neg-in |
| 43× | pow-pow |
| 34× | associate--l+ |
| 31× | diff-log |
| 29× | div-sub |
| 27× | sum-log |
| 25× | +-commutative pow-sub |
| 23× | pow-prod-up |
| 21× | sub-div |
| 20× | exp-prod |
| 13× | exp-sum pow-sqr |
| 12× | neg-sub0 associate--r+ pow-neg |
| 9× | pow-plus neg-mul-1 |
| 7× | unpow-prod-up |
| 6× | pow-flip pow2 inv-pow rem-exp-log |
| 5× | log-pow un-div-inv |
| 4× | associate--l- log-prod associate-+r- associate-+r+ distribute-frac-neg asin-acos acos-asin |
| 3× | sqrt-unprod |
| 2× | associate-+l+ exp-diff cos-sum rem-square-sqrt e-exp-1 |
| 1× | sqrt-undiv distribute-rgt-neg-out distribute-rgt-out-- cos-diff rem-log-exp |
Total 56.4b remaining (24.4%)
Threshold costs 4.0b (1.7%)
| 10.8b | 11.2% | Toniolo and Linder, Equation (13) |
| 8.1b | 13.9% | Maksimov and Kolovsky, Equation (3) |
| 7.9b | 45.1% | Henrywood and Agarwal, Equation (3) |
| 6.8b | 0% | Henrywood and Agarwal, Equation (12) |
| 5.6b | 76.4% | Toniolo and Linder, Equation (7) |