| 61× | intervals |
| 1.1m | 252279× | body | 80 | valid |
| 49.1s | 29162× | body | 1280 | valid |
| 41.4s | 160850× | body | 80 | nan |
| 27.2s | 20247× | body | 640 | valid |
| 18.6s | 8741× | body | 2560 | valid |
| 11.4s | 3344× | body | 5120 | valid |
| 9.4s | 10056× | body | 320 | valid |
| 4.8s | 9093× | body | 160 | valid |
| 1.9s | 864× | body | 10240 | exit |
| 1.4s | 645× | body | 640 | nan |
| 760.0ms | 662× | body | 1280 | nan |
| 289.0ms | 8256× | pre | 80 | true |
| 198.0ms | 365× | body | 320 | nan |
| 94.0ms | 194× | body | 160 | nan |
434 calls:
| 2.2s | (fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (* (/ M (/ (* 2 d) D)) (/ (* (cbrt h) (cbrt h)) 1)) (/ (cbrt h) l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h)))) |
| 2.2s | (fma (* (* (fabs (/ (cbrt d) (cbrt l))) (sqrt (/ (cbrt d) (cbrt l)))) (sqrt (/ d h))) (* (* (* (/ M (/ (* 2 d) D)) (/ h l)) (/ M (/ (* 2 d) D))) -1/2) (* (* (sqrt (/ 1 (* (cbrt l) (cbrt l)))) (sqrt (/ d (cbrt l)))) (sqrt (/ d h)))) |
| 2.0s | (/ (- 1 (* (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) (+ 1/2 (/ 1/2 (hypot 1 x))))) (fma (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (sqrt (+ (sqrt (+ 1/2 (/ 1/2 (hypot 1 x)))) 1)) (+ 1/2 (/ 1/2 (hypot 1 x))))) |
| 1.8s | (/ (/ (/ (sqrt (fma (* v v) -5 1)) PI) t) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2))))) |
| 1.8s | (/ (/ (/ (sqrt (fma (* v v) -5 1)) 1) 1) (* (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))) (cbrt (fma (sqrt (fma 6 (* (- v) v) 2)) (* (- v) v) (sqrt (fma 6 (* (- v) v) 2)))))) |
| 115× | rewrite-expression-head |
434 calls:
| 1.7s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 1.6s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 1.5s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 1.5s | (+ (sqrt (- (* (* (/ c0 w) (/ (* (/ d D) (/ d D)) h)) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) (* M M))) (* (/ c0 w) (/ (* (/ d D) (/ d D)) h))) |
| 1.4s | (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n))))) |
| 105367× | times-frac |
| 49753× | add-sqr-sqrt |
| 47163× | *-un-lft-identity |
| 46475× | add-cube-cbrt |
| 24957× | cbrt-prod |
| 7696× | add-exp-log |
| 6403× | prod-diff |
| 5699× | unpow-prod-up |
| 5579× | sqrt-prod |
| 5444× | add-cbrt-cube |
| 5219× | associate-*l* |
| 4315× | div-inv |
| 3981× | div-exp |
| 2806× | cbrt-undiv |
| 2099× | prod-exp |
| 2057× | associate-*r* |
| 1936× | pow1 |
| 1697× | cbrt-unprod |
| 1379× | associate-/r* |
| 1057× | associate-/l* |
| 884× | unpow-prod-down |
| 786× | associate-/r/ |
| 626× | unswap-sqr |
| 545× | add-log-exp |
| 527× | pow-prod-down |
| 437× | log1p-expm1-u |
| 435× | expm1-log1p-u |
| 434× | insert-posit16 |
| 357× | sqr-pow |
| 297× | swap-sqr |
| 275× | pow-prod-up |
| 253× | 1-exp |
| 249× | difference-of-squares |
| 230× | associate-*r/ |
| 218× | cbrt-div |
| 216× | distribute-lft-out-- |
| 212× | tan-quot |
| 197× | distribute-rgt-neg-in |
| 191× | distribute-lft-neg-in |
| 187× | sub-neg |
| 169× | distribute-rgt-in distribute-lft-in |
| 168× | sqrt-div |
| 161× | pow-sqr |
| 159× | sqrt-pow1 |
| 154× | associate-*l/ |
| 139× | frac-times |
| 138× | pow-exp |
| 136× | pow-plus |
| 133× | exp-sum |
| 126× | flip3-- flip-- |
| 123× | *-commutative |
| 118× | pow1/2 |
| 107× | frac-2neg clear-num |
| 106× | fma-neg |
| 89× | pow2 |
| 83× | distribute-lft-out |
| 77× | pow1/3 rec-exp |
| 72× | flip-+ flip3-+ |
| 71× | pow-to-exp |
| 69× | cos-sum |
| 67× | fma-def |
| 65× | rem-sqrt-square |
| 64× | associate-/l/ |
| 62× | fma-udef |
| 58× | exp-prod |
| 54× | pow-unpow |
| 51× | associate-+l+ |
| 43× | pow-sub |
| 41× | unpow2 |
| 40× | frac-add |
| 32× | associate--r+ |
| 30× | sum-log diff-log |
| 26× | pow-pow |
| 21× | neg-mul-1 |
| 20× | sqrt-undiv |
| 19× | +-commutative distribute-neg-frac |
| 12× | associate--l+ hypot-def |
| 11× | sqrt-unprod |
| 10× | frac-sub |
| 9× | pow-flip div-sub |
| 7× | inv-pow rem-exp-log |
| 6× | neg-log rem-square-sqrt |
| 5× | associate-+r+ cube-unmult acos-asin |
| 4× | expm1-log1p expm1-udef distribute-lft-neg-out pow3 remove-posit16 |
| 3× | neg-sub0 exp-diff distribute-rgt-out-- hypot-udef asin-acos cos-diff associate--r- |
| 2× | associate--l- distribute-rgt-neg-out log1p-expm1 sqrt-pow2 sqr-sin un-div-inv rem-cbrt-cube sin-mult log1p-udef |
| 1× | sub-div pow-neg |
Total 56.4b remaining (31.5%)
Threshold costs 4.5b (2.5%)
| 13.9b | -4.8% | Toniolo and Linder, Equation (13) |
| 8.8b | -0.4% | Henrywood and Agarwal, Equation (13) |
| 6.6b | 49.9% | Henrywood and Agarwal, Equation (3) |
| 6.2b | 74.3% | Toniolo and Linder, Equation (7) |
| 4.4b | -9.1% | Maksimov and Kolovsky, Equation (3) |