| 157× | rewrite-expression-head |
483 calls:
| 24.6s | (* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x) |
| 21.7s | (* (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (/ 1 (+ (+ (+ (+ (+ (+ 1.0 (* (/ 1737369620307813.0 2251799813685248.0) (* x x))) (* (/ 2620859570069187.0 9007199254740992.0) (* (* x x) (* x x)))) (* (/ 2502400853142105.0 3.602879701896397e+16) (* (* (* x x) (* x x)) (* x x)))) (* (/ 2017691060547333.0 1.4411518807585587e+17) (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* (/ 7681173503746455.0 9.223372036854776e+18) (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 (/ 825478423409049.0 4.611686018427388e+18)) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)) |
| 20.1s | (* (/ 1 (+ (+ (+ (+ (+ (+ 1.0 (* (/ 1737369620307813.0 2251799813685248.0) (* x x))) (* (/ 2620859570069187.0 9007199254740992.0) (* (* x x) (* x x)))) (* (/ 2502400853142105.0 3.602879701896397e+16) (* (* (* x x) (* x x)) (* x x)))) (* (/ 2017691060547333.0 1.4411518807585587e+17) (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* (/ 7681173503746455.0 9.223372036854776e+18) (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 (/ 825478423409049.0 4.611686018427388e+18)) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x) |
| 14.6s | (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) |
| 14.4s | (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) |
| 63994× | frac-add |
| 62905× | frac-times |
| 47534× | associate-*r/ |
| 12981× | associate-*l/ |
| 10922× | frac-sub |
| 8286× | flip-+ flip3-+ |
| 6200× | times-frac |
| 5782× | *-un-lft-identity |
| 5669× | add-sqr-sqrt |
| 4012× | add-exp-log |
| 3997× | add-cube-cbrt |
| 3215× | add-cbrt-cube |
| 2613× | pow1 |
| 1967× | prod-exp |
| 1574× | cbrt-unprod |
| 1564× | sqrt-prod |
| 1440× | associate-*r* |
| 1344× | associate-*l* |
| 1229× | pow-prod-down |
| 773× | add-log-exp |
| 769× | div-exp |
| 673× | distribute-lft-out |
| 525× | cbrt-prod |
| 517× | exp-diff |
| 515× | cbrt-div |
| 502× | cbrt-undiv |
| 500× | exp-neg |
| 497× | neg-sub0 |
| 463× | associate-/r/ |
| 433× | sqrt-div |
| 426× | associate-/l* |
| 384× | associate-/r* |
| 383× | cube-div |
| 372× | unswap-sqr |
| 341× | difference-of-squares |
| 312× | div-inv |
| 291× | unpow-prod-down |
| 272× | log-pow |
| 263× | sqrt-pow1 |
| 232× | distribute-lft-out-- |
| 214× | swap-sqr |
| 207× | pow-unpow |
| 178× | pow1/2 |
| 167× | associate-/l/ flip3-- flip-- |
| 153× | *-commutative |
| 141× | sqr-pow |
| 128× | pow-exp |
| 124× | log-prod distribute-neg-frac |
| 115× | cube-prod |
| 102× | pow-to-exp |
| 89× | pow-prod-up |
| 86× | diff-log |
| 83× | sub-neg |
| 79× | pow1/3 |
| 77× | frac-2neg clear-num |
| 75× | distribute-rgt-in sum-log distribute-lft-in |
| 66× | 1-exp rec-exp |
| 63× | rem-sqrt-square exp-prod |
| 60× | pow-sqr |
| 50× | pow-plus +-commutative |
| 44× | exp-sum |
| 38× | pow-pow inv-pow pow-flip |
| 28× | pow2 associate--l+ |
| 24× | div-sub |
| 21× | un-div-inv log-div |
| 19× | unpow3 cube-mult |
| 16× | sqrt-unprod |
| 15× | distribute-rgt-neg-in associate-+l+ |
| 14× | difference-of-sqr-1 |
| 13× | associate--l- |
| 12× | associate-+r+ |
| 10× | rem-exp-log associate--r+ |
| 9× | sum-cubes distribute-lft-neg-in |
| 8× | rem-cube-cbrt |
| 6× | sin-sum |
| 5× | e-exp-1 associate-+l- |
| 4× | distribute-neg-in rem-log-exp unpow2 |
| 3× | rem-square-sqrt rem-cbrt-cube neg-mul-1 |
| 2× | cos-sum sqrt-undiv difference-cubes sqrt-pow2 pow3 distribute-rgt-neg-out |
| 1× | associate-+r- distribute-rgt-out-- distribute-frac-neg log-rec neg-log |
| 95× | intervals |
| 1.2m | 11878× | body | 10240 | exit |
| 43.2s | 413274× | body | 80 | valid |
| 20.1s | 22393× | body | 1280 | valid |
| 8.3s | 17832× | body | 640 | valid |
| 6.0s | 1581× | body | 1280 | nan |
| 5.8s | 62247× | body | 80 | nan |
| 3.0s | 9070× | body | 320 | valid |
| 2.8s | 1351× | body | 640 | nan |
| 2.5s | 8938× | body | 160 | valid |
| 1.7s | 49536× | pre | 80 | true |
| 1.0s | 799× | body | 2560 | valid |
| 962.0ms | 636× | body | 320 | nan |
| 248.0ms | 290× | body | 5120 | valid |
| 230.0ms | 316× | body | 160 | nan |
480 calls:
| 26.8s | (- (pow 1.0 3) (/ (pow (* (* 1.0 (- (* (/ 2295300911148351.0 9007199254740992.0) (/ 2295300911148351.0 9007199254740992.0)) (* (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -5125037576950889.0 18014398509481984.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 6401478394306903.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -6544414927309881.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (/ 4780145094533421.0 4503599627370496.0)))))))) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -5125037576950889.0 18014398509481984.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 6401478394306903.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -6544414927309881.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (/ 4780145094533421.0 4503599627370496.0))))))))))) (exp 0)) 3) (pow (* (* (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x))) (- (/ 2295300911148351.0 9007199254740992.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -5125037576950889.0 18014398509481984.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 6401478394306903.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -6544414927309881.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (/ 4780145094533421.0 4503599627370496.0)))))))))) (exp (* (fabs x) (fabs x)))) 3))) |
| 4.8s | (- (pow 1.0 3) (pow (* (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 2295300911148351.0 9007199254740992.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -5125037576950889.0 18014398509481984.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 6401478394306903.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -6544414927309881.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (/ 4780145094533421.0 4503599627370496.0)))))))))) (exp (- (* (fabs x) (fabs x))))) 3)) |
| 3.1s | (/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) |
| 2.8s | (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) |
| 2.4s | (* (* (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 2295300911148351.0 9007199254740992.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -5125037576950889.0 18014398509481984.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 6401478394306903.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -6544414927309881.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (/ 4780145094533421.0 4503599627370496.0)))))))))) (exp (- (* (fabs x) (fabs x))))) (+ (* (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 2295300911148351.0 9007199254740992.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -5125037576950889.0 18014398509481984.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ 6401478394306903.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (+ (/ -6544414927309881.0 4503599627370496.0) (* (/ 1.0 (+ 1.0 (* (/ 1475339155889891.0 4503599627370496.0) (fabs x)))) (/ 4780145094533421.0 4503599627370496.0)))))))))) (exp (- (* (fabs x) (fabs x))))) 1.0)) |
Total 61.7b remaining (29.8%)
Threshold costs 5.0b (2.4%)
| 10.2b | 59% | math.log10 on complex, real part |
| 10.1b | 59.3% | math.log/1 on complex, real part |
| 9.9b | 58.9% | math.abs on complex |
| 9.1b | 56.9% | math.sqrt on complex, imaginary part, im greater than 0 branch |
| 5.5b | 15% | Octave 3.8, jcobi/2 |