365 calls:
| 6.7m | (/ (/ (- (* (* (* 1.0 (* 1.0 1.0)) (* (* 1.0 1.0) (* 1.0 1.0))) (* 1.0 1.0)) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))) (fma (* 1.0 (* 1.0 1.0)) (* 1.0 (* 1.0 1.0)) (* (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))) (fma 1.0 (* 1.0 1.0) (* (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)) (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0)))))))) (fma 1.0 1.0 (fma 1.0 (sqrt (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))) (+ (/ (* 0.5 1.0) (hypot 1.0 x)) (* 0.5 1.0))))) |
| 26.8s | (sqrt (* (* (cbrt U) (cbrt U)) (* (cbrt U) (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))) |
| 23.3s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))) |
| 23.1s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))) |
| 22.5s | (sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))) |
| 54× | intervals |
| 42.2s | 210528× | body | 80 | valid |
| 36.3s | 21729× | body | 1280 | valid |
| 21.6s | 103318× | body | 80 | nan |
| 19.8s | 17458× | body | 640 | valid |
| 10.0s | 3247× | body | 2560 | valid |
| 7.7s | 1075× | body | 5120 | valid |
| 6.5s | 8170× | body | 320 | valid |
| 4.1s | 8414× | body | 160 | valid |
| 495.0ms | 601× | body | 1280 | nan |
| 362.0ms | 627× | body | 640 | nan |
| 255.0ms | 343× | body | 320 | nan |
| 238.0ms | 8256× | pre | 80 | true |
| 199.0ms | 140× | body | 10240 | exit |
| 43.0ms | 171× | body | 160 | nan |
| 96× | rewrite-expression-head |
365 calls:
| 7.3s | (* (* (* (* (/ (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)) |
| 6.7s | (* (pow (/ 1 (pow t 1.0)) 1.0) (* (* (* (* (/ l (sin k)) (/ l (sin k))) (cos k)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))) |
| 6.5s | (* (* (* (/ (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)) |
| 5.7s | (/ 2.0 (* (* (* (/ (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))) |
| 4.7s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 95136× | add-exp-log |
| 69004× | prod-exp |
| 44056× | pow-exp |
| 32440× | div-exp |
| 14409× | times-frac |
| 14361× | pow-to-exp |
| 8941× | 1-exp |
| 8937× | rec-exp |
| 8204× | add-sqr-sqrt |
| 7725× | *-un-lft-identity |
| 7165× | add-cube-cbrt |
| 3777× | unpow-prod-down |
| 3218× | sqrt-prod |
| 2729× | add-cbrt-cube |
| 1246× | cbrt-unprod |
| 1240× | pow1 |
| 1182× | associate-*l* |
| 981× | div-inv |
| 952× | frac-times |
| 877× | associate-*r/ |
| 801× | associate-*r* |
| 706× | sqr-pow |
| 698× | prod-diff |
| 631× | associate-*l/ |
| 606× | cbrt-undiv |
| 567× | associate-/r/ |
| 533× | tan-quot |
| 525× | flip-+ flip3-+ |
| 420× | associate-/r* |
| 415× | pow-prod-down add-log-exp |
| 395× | associate-/l* |
| 365× | expm1-log1p-u log1p-expm1-u insert-posit16 |
| 290× | unswap-sqr |
| 285× | sqrt-div |
| 277× | cbrt-prod |
| 254× | distribute-rgt-in distribute-lft-in |
| 224× | distribute-lft-out |
| 192× | sqrt-pow1 |
| 180× | pow-unpow |
| 134× | difference-of-squares |
| 124× | *-commutative |
| 115× | pow1/2 |
| 108× | distribute-lft-out-- |
| 105× | swap-sqr |
| 91× | rem-sqrt-square |
| 82× | frac-2neg clear-num |
| 79× | flip3-- flip-- |
| 68× | pow-prod-up |
| 66× | exp-prod |
| 58× | fma-neg |
| 52× | sub-neg |
| 44× | associate-/l/ |
| 42× | pow1/3 |
| 32× | pow-sqr |
| 29× | fma-def |
| 27× | associate-+r+ pow-pow |
| 26× | distribute-rgt-neg-in distribute-lft-neg-in |
| 25× | associate--l+ cos-sum |
| 18× | frac-add |
| 17× | div-sub diff-log |
| 16× | pow-plus |
| 15× | associate-+l- |
| 14× | pow2 |
| 13× | fma-udef |
| 12× | neg-sub0 pow-sub hypot-def pow-neg |
| 11× | pow3 |
| 8× | pow-flip sum-log associate--r+ inv-pow |
| 7× | +-commutative |
| 5× | cbrt-div difference-cubes distribute-rgt-out-- |
| 4× | frac-sub |
| 3× | exp-diff cube-unmult hypot-udef unpow2 asin-acos rem-exp-log log-pow count-2 distribute-rgt-out |
| 2× | associate--l- sqrt-unprod neg-mul-1 rem-square-sqrt unpow1/3 |
| 1× | cos-mult associate-+r- sub-div un-div-inv sqr-cos acos-asin cos-diff |
Total 45.6b remaining (32.8%)
Threshold costs 3.4b (2.4%)
| 9.5b | -11.9% | Toniolo and Linder, Equation (10+) |
| 6.2b | 38.5% | Toniolo and Linder, Equation (10-) |
| 5.6b | 54.9% | Henrywood and Agarwal, Equation (3) |
| 5.4b | 77.1% | Toniolo and Linder, Equation (7) |
| 5.0b | 21.1% | Henrywood and Agarwal, Equation (12) |