| 100× | intervals |
| 1.1m | 496506× | body | 80 | valid |
| 58.7s | 15777× | body | 10240 | exit |
| 32.0s | 30244× | body | 1280 | valid |
| 15.4s | 23335× | body | 640 | valid |
| 7.8s | 69884× | body | 80 | nan |
| 6.4s | 12089× | body | 320 | valid |
| 5.6s | 3076× | body | 1280 | nan |
| 3.8s | 2577× | body | 640 | nan |
| 2.6s | 10086× | body | 160 | valid |
| 1.5s | 49536× | pre | 80 | true |
| 1.2s | 1284× | body | 320 | nan |
| 871.0ms | 1423× | body | 2560 | valid |
| 372.0ms | 617× | body | 160 | nan |
| 349.0ms | 617× | body | 5120 | valid |
| 156× | rewrite-expression-head |
476 calls:
| 1.5m | (* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)))))) |
| 23.6s | (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) |
| 5.4s | (/ (/ (fma -1259.1392167224028 (* (* (- 3.0 z) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (* (* (- 5.0 z) (- 8.0 z)) (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))))) (* (+ (- z) 2.0) (fma (fma (- (* (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (* (/ -176.6150291621406 (- 4.0 z)) (/ -176.6150291621406 (- 4.0 z)))) (- 3.0 z) (* (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z))) 771.3234287776531)) (* (* (- 5.0 z) (- 8.0 z)) (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z)))) (* (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z))) (* (- 3.0 z) (fma 12.507343278686905 (* (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))) (- 8.0 z)) (* (- 5.0 z) (fma 1.5056327351493116e-07 (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))) (* (- (* (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ 9.984369578019572e-06 (+ (- z) 7.0))) (* (/ -0.13857109526572012 (- 6.0 z)) (/ -0.13857109526572012 (- 6.0 z)))) (- 8.0 z)))))))))) (* (+ (- z) 2.0) (* (* (- 3.0 z) (- (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (* (* (- 5.0 z) (- 8.0 z)) (- (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z))))))) (exp (+ 0.5 (+ (- z) 7.0)))) |
| 3.2s | (/ (* (- (- z) 2.0) (* (* (+ 3.0 z) (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (- 4.0 z)))) (* (* (+ (* 5.0 5.0) (+ (* z z) (* 5.0 z))) (+ (* 8.0 8.0) (+ (* z z) (* 8.0 z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (- 6.0 z)))))) (exp (+ (- z) 7.0))) |
| 3.1s | (* (* (sqrt (/ 1 PI)) (exp (pow (fabs x) 2))) (+ (+ (+ (/ 1.0 (fabs x)) (/ 0.75 (pow (fabs x) 5))) (/ 1.875 (pow (fabs x) 7))) (/ 0.5 (pow (fabs x) 3)))) |
| 31517× | frac-times |
| 17092× | times-frac |
| 13625× | *-un-lft-identity |
| 12376× | flip3-- flip-- |
| 9899× | add-sqr-sqrt |
| 9694× | associate-*r/ |
| 8294× | associate-/r/ |
| 7492× | add-cube-cbrt |
| 7463× | flip-+ flip3-+ |
| 6018× | associate-*l/ |
| 5266× | frac-sub |
| 2644× | distribute-lft-out |
| 2311× | sqrt-prod |
| 2303× | associate-/l* |
| 2249× | add-exp-log |
| 1935× | frac-add |
| 1819× | exp-sum |
| 1728× | add-cbrt-cube |
| 1703× | associate-/l/ |
| 1378× | pow1 |
| 1093× | prod-diff |
| 1049× | associate-*l* |
| 1007× | associate-*r* |
| 727× | add-log-exp |
| 697× | prod-exp |
| 691× | distribute-lft-out-- |
| 689× | difference-of-squares |
| 579× | cbrt-prod |
| 571× | associate-/r* |
| 547× | div-exp |
| 482× | log1p-expm1-u |
| 477× | cbrt-unprod |
| 476× | expm1-log1p-u |
| 442× | unpow-prod-down |
| 394× | div-inv |
| 361× | unswap-sqr |
| 353× | cbrt-undiv |
| 327× | swap-sqr |
| 321× | pow-prod-down |
| 257× | cube-prod |
| 202× | fma-def |
| 175× | distribute-rgt-in distribute-lft-in |
| 171× | sqrt-pow1 |
| 168× | sqr-pow |
| 158× | log-pow |
| 151× | fma-neg |
| 129× | *-commutative |
| 124× | sum-log |
| 118× | cbrt-div |
| 103× | frac-2neg clear-num distribute-rgt-neg-in |
| 100× | pow1/2 |
| 93× | pow1/3 |
| 90× | pow-exp |
| 89× | pow-unpow |
| 86× | distribute-lft-neg-in |
| 75× | sqrt-div |
| 74× | 1-exp |
| 73× | unpow3 cube-mult |
| 72× | rec-exp |
| 62× | pow-prod-up |
| 60× | sub-neg |
| 55× | fma-udef |
| 53× | pow-to-exp associate--l+ |
| 46× | pow-sqr |
| 45× | log-prod |
| 44× | diff-log associate-+l+ |
| 40× | rem-sqrt-square |
| 36× | pow-pow |
| 35× | associate-+l- |
| 31× | exp-prod |
| 27× | pow-plus +-commutative |
| 25× | exp-diff |
| 23× | pow2 |
| 22× | neg-mul-1 |
| 21× | rem-cube-cbrt |
| 16× | div-sub |
| 14× | hypot-udef |
| 13× | cube-div |
| 12× | un-div-inv pow-flip neg-sub0 |
| 10× | inv-pow |
| 9× | exp-neg expm1-udef |
| 8× | sqrt-unprod expm1-log1p associate--r+ |
| 6× | log1p-udef rem-log-exp associate--l- |
| 5× | associate-+r+ |
| 4× | log1p-expm1 distribute-neg-in pow-sub rem-square-sqrt |
| 3× | unpow-prod-up hypot-def rem-cbrt-cube |
| 2× | distribute-rgt-neg-out |
| 1× | rem-exp-log difference-cubes sqrt-pow2 sum-cubes associate-+r- pow3 sin-sum sub-div distribute-frac-neg cos-sum associate--r- unpow2 |
476 calls:
| 11.3s | (+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3)) |
| 4.4s | (* (+ (sqrt (* d1 (- (+ d4 d2) d3))) d1) (- (sqrt (* d1 (- (+ d4 d2) d3))) d1)) |
| 1.7s | (- (pow 1.0 3) (log1p (expm1 (log (exp (pow (* (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) (/ (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (exp (pow (fabs x) 2)))) 3)))))) |
| 1.7s | (* (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5)))))) (cbrt (* (/ (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (* (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))) (/ (sqrt (* PI 2.0)) (cbrt (exp (+ (+ (- z 1.0) 7.0) 0.5))))))) |
| 1.6s | (* (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0)) (sqrt (/ (pow (* -2.0 (log u1)) 0.5) 6.0))) |
Total 24.2b remaining (18.4%)
Threshold costs 8.8b (6.7%)
| 9.1b | 17.6% | _divideComplex, real part |
| 2.9b | 77.4% | Octave 3.8, jcobi/1 |
| 2.4b | 31.3% | Octave 3.8, jcobi/4 |
| 1.1b | 0% | Jmat.Real.lambertw, newton loop step |
| 0.9b | 60.8% | Octave 3.8, jcobi/3 |