| 90× | intervals |
| 6.5m | 100771× | body | 10240 | exit |
| 1.1m | 398158× | body | 80 | valid |
| 38.1s | 26187× | body | 1280 | valid |
| 19.0s | 20296× | body | 640 | valid |
| 11.6s | 70024× | body | 80 | nan |
| 6.9s | 10678× | body | 320 | valid |
| 5.5s | 1670× | body | 1280 | nan |
| 4.7s | 9516× | body | 160 | valid |
| 3.7s | 1380× | body | 640 | nan |
| 2.6s | 49536× | pre | 80 | true |
| 1.6s | 1426× | body | 2560 | valid |
| 1.4s | 662× | body | 320 | nan |
| 818.0ms | 337× | body | 160 | nan |
| 567.0ms | 628× | body | 5120 | valid |
| 146× | rewrite-expression-head |
454 calls:
| 1.2m | (* (sqrt (* 2 PI)) (* (* (/ (pow (+ (- 7 z) 0.5) (+ 0.5 (- 0 z))) (exp (+ (- 7 z) 0.5))) (+ (+ (+ (/ 1.5056327351493116e-07 (- 8 z)) (/ 9.984369578019572e-06 (- 7 z))) (+ (+ (/ -0.13857109526572012 (- 6 z)) 0.9999999999998099) (+ (/ 676.5203681218851 (- 1 z)) (+ (/ -1259.1392167224028 (- 2 z)) (/ 771.3234287776531 (- 3 z)))))) (+ (/ -176.6150291621406 (- 4 z)) (/ 12.507343278686905 (- 5 z))))) (/ PI (sin (* PI z))))) |
| 24.3s | (* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ z 0.5) -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099))) |
| 24.3s | (* (/ (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (exp (- -6))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099))) |
| 24.2s | (* (/ (* (pow (- (+ z 0.5) -6) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ z 0.5))) (+ (+ (+ (/ -0.13857109526572012 (- (+ 6 z) 1)) (/ 12.507343278686905 (+ z 4))) (+ (/ 9.984369578019572e-06 (+ 6 z)) (/ 1.5056327351493116e-07 (+ 7 z)))) (+ (+ (/ 676.5203681218851 z) (+ (/ -176.6150291621406 (- z -3)) (+ (/ 771.3234287776531 (+ 2 z)) (/ -1259.1392167224028 (+ z 1))))) 0.9999999999998099))) |
| 16.4s | (* (/ (+ (+ (+ (+ (+ 1 (* 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 (* 0.7715471019 (* 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 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x) |
| 3743181× | frac-times |
| 3263046× | frac-add |
| 2078268× | flip-+ flip3-+ |
| 1849278× | frac-sub |
| 1445131× | flip3-- flip-- |
| 1383514× | associate-*l/ |
| 1314724× | associate-*r/ |
| 52977× | *-un-lft-identity |
| 42144× | times-frac |
| 21421× | add-sqr-sqrt |
| 20163× | distribute-lft-out |
| 17272× | add-cube-cbrt |
| 14301× | sqrt-prod |
| 4987× | prod-diff |
| 3398× | add-exp-log |
| 3056× | associate-*r* |
| 3027× | pow1 |
| 2769× | distribute-rgt-in distribute-lft-in |
| 2406× | add-cbrt-cube |
| 1670× | associate-/r/ |
| 1573× | difference-of-squares |
| 1517× | associate-*l* |
| 1502× | prod-exp |
| 1460× | distribute-lft-out-- |
| 1364× | associate-/l* |
| 1029× | cbrt-unprod |
| 1011× | div-inv |
| 890× | pow-prod-down |
| 824× | div-exp |
| 614× | add-log-exp |
| 611× | sqrt-div |
| 610× | pow-prod-up |
| 592× | associate-/r* |
| 533× | fma-def |
| 455× | expm1-log1p-u |
| 454× | insert-posit16 log1p-expm1-u |
| 431× | cbrt-undiv |
| 425× | cbrt-div |
| 363× | exp-sum |
| 321× | unswap-sqr |
| 279× | log-prod |
| 268× | cbrt-prod |
| 249× | pow-plus |
| 202× | swap-sqr |
| 200× | unpow-prod-down |
| 193× | pow-sqr |
| 184× | pow-div |
| 174× | fma-neg |
| 171× | *-commutative |
| 170× | log-pow |
| 148× | pow2 |
| 145× | pow-exp |
| 133× | associate-/l/ |
| 117× | 1-exp |
| 105× | rec-exp |
| 104× | pow-flip |
| 102× | frac-2neg clear-num |
| 100× | inv-pow |
| 92× | sqrt-pow1 |
| 91× | sub-neg |
| 73× | pow1/2 |
| 69× | associate--r+ |
| 67× | sqr-pow pow-to-exp |
| 64× | pow1/3 |
| 55× | fma-udef |
| 46× | sum-log exp-prod |
| 44× | diff-log |
| 25× | pow3 |
| 22× | cube-unmult div-sub |
| 19× | rem-sqrt-square |
| 18× | +-commutative |
| 16× | un-div-inv distribute-rgt-out |
| 13× | distribute-rgt1-in hypot-udef |
| 11× | sin-sum |
| 10× | rem-log-exp |
| 9× | associate--l+ hypot-def |
| 8× | unpow-prod-up exp-diff associate-+l- sin-mult |
| 7× | associate-+l+ sqrt-unprod pow-sub |
| 6× | pow-unpow |
| 5× | log-div |
| 4× | pow-pow associate--r- |
| 3× | associate-+r+ distribute-lft-neg-in distribute-rgt-neg-in rem-exp-log rem-square-sqrt |
| 2× | neg-sub0 sub0-neg sqr-sin exp-to-pow distribute-rgt-out-- exp-neg distribute-neg-in rem-cbrt-cube |
| 1× | expm1-log1p expm1-udef associate--l- associate-+r- distribute-rgt-neg-out log1p-expm1 neg-mul-1 cos-sum log1p-udef unsub-neg |
454 calls:
| 3.3s | (* (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) 1)) (/ (sqrt (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i)))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) |
| 3.2s | (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (/ (+ (+ alpha beta) (* 2 i)) (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) |
| 3.2s | (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) |
| 2.0s | (* (cbrt (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) -0.284496736)) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (- (* (fabs x) (fabs x))))))) (cbrt (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) -0.284496736)) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (exp (- (* (fabs x) (fabs x)))))))) |
| 1.4s | (* (pow (* -2 (log u1)) 0.5) 1/6) |
Total 32.4b remaining (27.5%)
Threshold costs 4.3b (3.6%)
| 6.9b | 33.2% | _divideComplex, imaginary part |
| 6.9b | 36.1% | _divideComplex, real part |
| 5.3b | 15.8% | Octave 3.8, jcobi/2 |
| 3.2b | 74.4% | Octave 3.8, jcobi/1 |
| 1.7b | 0% | Jmat.Real.lambertw, newton loop step |