| 164× | rewrite-expression-head |
505 calls:
| 1.2m | (* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0)))) |
| 48.4s | (* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (exp (+ (* (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5))) (log (sqrt (* PI 2.0)))))) |
| 46.5s | (/ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (/ (exp z) (exp (fma (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5)) (log (sqrt (* PI 2.0))))))) |
| 44.8s | (* (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (/ (exp (- (- 1.0 7.0) 0.5)) (exp (- z (fma (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5)) (log (sqrt (* PI 2.0)))))))) |
| 44.2s | (* (/ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 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)))))) (/ (exp z) (exp (fma (+ (- z 1.0) 0.5) (log (+ (+ (- z 1.0) 7.0) 0.5)) (log (sqrt (* PI 2.0))))))) (exp (- (- 1.0 7.0) 0.5))) |
| 23817× | times-frac |
| 20520× | *-un-lft-identity |
| 13450× | add-sqr-sqrt |
| 12122× | add-cube-cbrt |
| 5568× | distribute-lft-out |
| 5484× | sqrt-prod |
| 5051× | add-exp-log |
| 4499× | pow1 |
| 4000× | add-cbrt-cube |
| 2980× | frac-add |
| 2941× | prod-exp |
| 2302× | cbrt-unprod |
| 2243× | pow-prod-down |
| 1893× | prod-diff |
| 1706× | associate-*r* |
| 1698× | associate-*l* |
| 1059× | exp-sum |
| 1046× | flip-+ flip3-+ |
| 829× | div-inv |
| 822× | add-log-exp |
| 776× | associate-*l/ |
| 725× | div-exp |
| 697× | pow-prod-up |
| 671× | associate-/l* |
| 626× | sqrt-pow1 |
| 597× | associate-/r* |
| 507× | log1p-expm1-u |
| 506× | expm1-log1p-u |
| 454× | cbrt-undiv |
| 410× | frac-times |
| 363× | associate-/l/ |
| 339× | unswap-sqr |
| 307× | cbrt-prod |
| 301× | associate--l+ |
| 297× | distribute-rgt-in distribute-lft-in |
| 293× | log-pow |
| 272× | difference-of-squares |
| 270× | associate-*r/ |
| 266× | pow1/2 |
| 259× | pow-plus |
| 251× | swap-sqr |
| 247× | distribute-lft-out-- |
| 233× | associate-/r/ pow-sqr |
| 227× | pow1/3 |
| 221× | log-prod |
| 216× | flip3-- flip-- |
| 212× | fma-udef |
| 175× | fma-neg |
| 171× | cbrt-div |
| 168× | *-commutative |
| 162× | sub-neg |
| 149× | associate-+l- |
| 148× | sum-log |
| 143× | pow-sub |
| 139× | pow-exp |
| 136× | fma-def |
| 109× | sqrt-div |
| 104× | pow2 |
| 95× | frac-2neg clear-num |
| 94× | exp-prod |
| 73× | pow-to-exp |
| 66× | 1-exp |
| 63× | diff-log |
| 60× | distribute-rgt-out |
| 58× | rec-exp |
| 40× | associate-+l+ |
| 37× | unpow-prod-down |
| 36× | associate-+r+ pow-flip |
| 34× | +-commutative |
| 32× | sqr-pow |
| 26× | rem-sqrt-square |
| 24× | cube-unmult |
| 22× | distribute-rgt1-in frac-sub |
| 19× | pow-unpow |
| 18× | sqrt-unprod |
| 16× | distribute-rgt-neg-in div-sub distribute-lft-neg-in |
| 15× | rem-log-exp |
| 14× | exp-diff |
| 13× | hypot-udef |
| 12× | associate--l- |
| 10× | inv-pow |
| 9× | count-2 |
| 8× | distribute-lft1-in pow3 |
| 7× | hypot-def log-div |
| 6× | pow-pow un-div-inv cos-sum |
| 5× | associate--r+ rem-square-sqrt |
| 4× | sin-sum neg-mul-1 |
| 3× | expm1-log1p expm1-udef exp-to-pow |
| 2× | rem-exp-log associate--r- |
| 1× | unpow-prod-up associate-+r- log1p-expm1 log-rec distribute-rgt-out-- rem-cbrt-cube log1p-udef |
| 100× | intervals |
| 1.4m | 16169× | body | 10240 | exit |
| 54.8s | 459773× | body | 80 | valid |
| 32.3s | 31044× | body | 1280 | valid |
| 15.2s | 23726× | body | 640 | valid |
| 6.7s | 69248× | body | 80 | nan |
| 6.0s | 3116× | body | 1280 | nan |
| 5.4s | 2701× | body | 640 | nan |
| 5.2s | 11802× | body | 320 | valid |
| 3.6s | 10206× | body | 160 | valid |
| 1.7s | 1222× | body | 320 | nan |
| 1.5s | 49536× | pre | 80 | true |
| 1.0s | 1531× | body | 2560 | valid |
| 734.0ms | 597× | body | 5120 | valid |
| 419.0ms | 698× | body | 160 | nan |
505 calls:
| 7.5s | (- (* 1.0 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 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))) (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))) |
| 1.7s | (- 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 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))) |
| 1.5s | (* (sqrt (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (+ (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) |
| 1.2s | (/ (- (* (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2)))) (* 0.5 0.5)) (- (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5)) |
| 1.1s | (- 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 (* 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)))))) |
Total 31.3b remaining (21.9%)
Threshold costs 5.7b (4%)
| 7.5b | 34.2% | _divideComplex, real part |
| 5.9b | 13.7% | Octave 3.8, jcobi/2 |
| 3.4b | 0% | _divideComplex, imaginary part |
| 3.1b | 75.5% | Octave 3.8, jcobi/1 |
| 2.6b | 29.4% | Octave 3.8, jcobi/4 |