| 158× | rewrite-expression-head |
475 calls:
| 1.5m | (+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) |
| 1.5m | (+ (/ -176.6150291621406 (+ 4.0 (- z))) (+ (+ (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (+ (/ 771.3234287776531 (+ (- z) 3.0)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) |
| 46.1s | (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) z) (sqrt (* PI 2.0))) (* (exp (+ (+ (- z 1.0) 7.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (- 1.0 0.5)))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))) |
| 45.9s | (* (exp (log (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) z) (sqrt (* PI 2.0))) (* (exp (+ (+ (- z 1.0) 7.0) 0.5)) (pow (+ (+ (- z 1.0) 7.0) 0.5) 1.0))))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) 0.5) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))))) |
| 43.0s | (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ -1259.1392167224028 (+ (- z 1.0) 2.0)))) (+ (/ 771.3234287776531 (+ (- z 1.0) 3.0)) (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))) |
| 104496× | frac-add |
| 97819× | frac-times |
| 57937× | times-frac |
| 38706× | flip-+ flip3-+ |
| 34415× | *-un-lft-identity |
| 30636× | flip-- flip3-- |
| 28403× | associate-*r/ |
| 28109× | frac-sub |
| 24661× | add-sqr-sqrt |
| 22821× | associate-*l/ |
| 22590× | add-cube-cbrt |
| 12460× | sqrt-prod |
| 5789× | distribute-lft-out |
| 3000× | associate-/r/ |
| 2477× | add-exp-log |
| 1692× | add-cbrt-cube |
| 1665× | div-inv |
| 1634× | associate-*l* |
| 1436× | associate-*r* |
| 1423× | pow1 |
| 1376× | sqrt-div |
| 950× | prod-exp |
| 885× | add-log-exp |
| 830× | unpow-prod-down |
| 705× | associate-/l* |
| 614× | difference-of-squares |
| 584× | div-exp |
| 553× | associate-/r* |
| 477× | cbrt-prod |
| 463× | cbrt-unprod |
| 336× | distribute-lft-out-- |
| 320× | cbrt-undiv |
| 294× | pow-prod-down |
| 290× | unswap-sqr |
| 261× | cube-prod |
| 239× | log-pow |
| 225× | sqr-pow |
| 219× | pow-exp |
| 218× | sum-log |
| 193× | cbrt-div |
| 175× | pow-to-exp |
| 146× | *-commutative |
| 144× | sqrt-pow1 |
| 141× | log-prod |
| 134× | swap-sqr |
| 130× | associate-/l/ |
| 118× | pow1/2 |
| 117× | exp-diff |
| 99× | distribute-rgt-in distribute-lft-in |
| 96× | log-div |
| 89× | clear-num frac-2neg |
| 86× | pow1/3 |
| 79× | pow-unpow |
| 71× | exp-prod |
| 68× | sub-neg |
| 65× | rem-sqrt-square |
| 63× | pow-prod-up |
| 61× | +-commutative |
| 59× | exp-sum |
| 46× | diff-log |
| 43× | pow-sqr |
| 41× | 1-exp rec-exp |
| 34× | pow-plus |
| 33× | associate-+l- |
| 28× | pow-pow |
| 22× | pow2 |
| 20× | unpow3 cube-mult |
| 19× | div-sub |
| 17× | pow-flip associate-+r+ |
| 16× | associate--l+ |
| 11× | rem-log-exp |
| 10× | rem-cube-cbrt pow-sub |
| 9× | cube-div inv-pow unpow-prod-up associate--r+ |
| 8× | rem-exp-log |
| 6× | pow-div associate-+l+ |
| 5× | difference-cubes |
| 4× | un-div-inv distribute-neg-frac |
| 3× | sqrt-undiv distribute-lft-neg-in pow3 sin-sum sum-cubes distribute-rgt-neg-in |
| 2× | sqrt-unprod distribute-neg-in distribute-rgt-out-- rem-square-sqrt associate--r- rem-cbrt-cube |
| 1× | cos-sum e-exp-1 remove-double-div neg-mul-1 distribute-rgt-neg-out exp-to-pow associate--l- unpow2 |
475 calls:
| 2.5s | (* (sqrt (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (sqrt (/ (/ (* 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))))) |
| 2.2s | (* (/ (/ (* 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)))) |
| 1.9s | (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (* (- 1.0 (* 0.3275911 (fabs x))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x)))))) |
| 1.2s | (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (sqrt (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))) (* (sqrt (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x))))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (exp (- (* (fabs x) (fabs x)))))) |
| 1.1s | (* (sqrt (/ (/ (* 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)))) |
| 99× | intervals |
| 18.4s | 468872× | body | 80 | valid |
| 13.7s | 30619× | body | 1280 | valid |
| 6.3s | 11736× | body | 10240 | exit |
| 6.0s | 22638× | body | 640 | valid |
| 2.5s | 70940× | body | 80 | nan |
| 2.1s | 11975× | body | 320 | valid |
| 1.1s | 10186× | body | 160 | valid |
| 980.0ms | 1587× | body | 1280 | nan |
| 614.0ms | 1301× | body | 640 | nan |
| 604.0ms | 49536× | pre | 80 | true |
| 347.0ms | 1509× | body | 2560 | valid |
| 231.0ms | 667× | body | 320 | nan |
| 136.0ms | 576× | body | 5120 | valid |
| 78.0ms | 335× | body | 160 | nan |
Total 99.5b remaining (35.6%)
Threshold costs 3.9b (1.4%)
| 16.8b | 49.8% | math.sqrt on complex, imaginary part, im greater than 0 branch |
| 10.5b | 58.2% | math.log/2 on complex, real part |
| 10.2b | 57.9% | math.log10 on complex, real part |
| 10.1b | 58.4% | math.log/1 on complex, real part |
| 9.9b | 57.8% | math.abs on complex |