10611 calls:
| 2.3s | (/ (/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))) |
| 2.3s | (/ (/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i)) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (* (+ (+ alpha beta) i) i))) (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))) |
| 2.0s | (/ (/ (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta)))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))) |
| 1.9s | (* 1 (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (pow (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ z 1))) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (+ (/ -176.6150291621406 (+ z 3)) (+ (/ -0.13857109526572012 (- z -5)) (/ 12.507343278686905 (+ z 4))))) 3) (pow (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) 3)))) |
| 1.9s | (/ (/ (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (/ (* (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta))) (* (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) (fma 2 i (+ alpha beta)))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ alpha beta) i) i)))) (* (* (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0)) (- (* (fma 2 i (+ alpha beta)) (fma 2 i (+ alpha beta))) 1.0))) |
| 89× | intervals |
| 6.4m | 99178× | body | 10240 | exit |
| 1.2m | 402276× | body | 80 | valid |
| 26.2s | 22952× | body | 1280 | valid |
| 13.2s | 17867× | body | 640 | valid |
| 10.0s | 69421× | body | 80 | nan |
| 6.6s | 1573× | body | 1280 | nan |
| 4.3s | 9643× | body | 320 | valid |
| 3.9s | 1305× | body | 640 | nan |
| 2.5s | 49536× | pre | 80 | true |
| 1.9s | 1383× | body | 2560 | valid |
| 1.7s | 673× | body | 320 | nan |
| 1.6s | 5012× | body | 160 | valid |
| 539.0ms | 631× | body | 5120 | valid |
| 418.0ms | 325× | body | 160 | nan |
416 calls:
| 6.0s | (- (pow 1 3) (pow (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))) 3)) |
| 3.8s | (+ (* (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))) (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))) (* 1 (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ (* (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1))) (sqrt (/ 1.061405429 (fma 0.3275911 (fabs x) 1)))) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))) (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x)))))) |
| 1.5s | (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) |
| 1.5s | (pow (* (pow (- (log u1)) 1.0) (* (pow -2 1.0) (pow -1 1.0))) 0.5) |
| 926.0ms | (* 1/6 (pow (* -2 (log u1)) 0.5)) |
| 143× | rewrite-expression-head |
416 calls:
| 3.0s | (* (* (sqrt (* PI 2)) (pow (+ (- z -6) 0.5) z)) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ -1259.1392167224028 (+ z 1)) (+ (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ 12.507343278686905 (+ 4 z))) (+ (/ -0.13857109526572012 (+ z 5)) (/ -176.6150291621406 (+ z 3)))) (/ 771.3234287776531 (+ z 2)))))) |
| 1.7s | (* (exp (- (+ (- z -6) 0.5))) (* (* (pow (+ (- z -6) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (+ (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (/ -1259.1392167224028 (+ z 1))) (+ 0.9999999999998099 (/ 676.5203681218851 z))) (+ (/ -176.6150291621406 (+ z 3)) (+ (/ -0.13857109526572012 (- z -5)) (/ 12.507343278686905 (+ z 4))))) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7)))))) |
| 1.6s | (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) |
| 1.5s | (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) |
| 1.5s | (/ (* (* (sqrt (* PI 2)) (pow (+ (- z -6) 0.5) z)) (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (/ -1259.1392167224028 (+ z 1)) (+ (+ (+ (+ (/ 676.5203681218851 z) 0.9999999999998099) (/ 12.507343278686905 (+ 4 z))) (+ (/ -0.13857109526572012 (+ z 5)) (/ -176.6150291621406 (+ z 3)))) (/ 771.3234287776531 (+ z 2)))))) (* (exp (+ (- z -6) 0.5)) (pow (+ (- z -6) 0.5) (- 1 0.5)))) |
| 4844× | times-frac |
| 3586× | *-un-lft-identity |
| 3539× | add-sqr-sqrt |
| 3537× | frac-add |
| 3460× | add-cube-cbrt |
| 1575× | add-exp-log |
| 1529× | frac-times |
| 1508× | flip-+ flip3-+ |
| 1177× | associate-*r/ |
| 1080× | add-cbrt-cube |
| 1048× | pow1 |
| 983× | associate-*l/ |
| 827× | sqrt-prod |
| 648× | associate-*l* |
| 611× | prod-diff |
| 561× | associate-*r* |
| 514× | add-log-exp |
| 489× | prod-exp |
| 486× | associate-/r* |
| 454× | div-inv |
| 426× | associate-/l* |
| 416× | expm1-log1p-u insert-posit16 log1p-expm1-u |
| 395× | associate-+l- |
| 392× | pow-sub |
| 346× | associate-/r/ |
| 332× | div-exp |
| 322× | cbrt-div |
| 314× | unpow-prod-down |
| 285× | cube-prod |
| 271× | exp-diff |
| 268× | exp-neg neg-sub0 |
| 233× | cbrt-prod |
| 231× | cbrt-unprod |
| 199× | cbrt-undiv |
| 195× | pow-prod-down |
| 155× | pow-prod-up |
| 141× | rec-exp |
| 134× | flip3-- associate-/l/ flip-- |
| 132× | fma-def |
| 120× | *-commutative |
| 118× | cube-mult |
| 117× | unpow3 |
| 104× | pow-div |
| 99× | fma-neg |
| 89× | frac-2neg clear-num |
| 86× | sub-neg |
| 79× | sqrt-div |
| 74× | distribute-rgt-in distribute-lft-in |
| 73× | pow-flip inv-pow |
| 72× | pow1/3 |
| 71× | pow-exp |
| 68× | distribute-lft-out |
| 64× | log-pow |
| 62× | pow1/2 fma-udef |
| 61× | pow-to-exp |
| 55× | pow-plus |
| 43× | pow2 |
| 35× | difference-of-squares |
| 34× | +-commutative |
| 32× | log-prod |
| 30× | exp-prod |
| 29× | associate--l+ |
| 28× | exp-sum |
| 27× | sum-log |
| 26× | diff-log |
| 22× | frac-sub |
| 19× | rem-sqrt-square |
| 18× | un-div-inv |
| 16× | distribute-lft-out-- div-sub |
| 14× | distribute-rgt-out |
| 13× | associate-+l+ pow-pow |
| 12× | associate--l- sin-sum |
| 11× | distribute-rgt1-in difference-of-sqr-1 expm1-def |
| 9× | hypot-def |
| 7× | cube-unmult pow3 sqrt-unprod |
| 6× | rem-cube-cbrt difference-cubes |
| 5× | neg-mul-1 cube-div |
| 4× | associate-+r+ rem-log-exp rem-cbrt-cube |
| 3× | unpow-prod-up associate-+r- associate--r+ rem-square-sqrt |
| 2× | sum-cubes rem-exp-log unsub-neg |
| 1× | remove-posit16 distribute-lft1-in hypot-udef cos-sum distribute-neg-in associate--r- distribute-rgt-out-- log-div |
Total 28.9b remaining (21.9%)
| 8.9b | 20.3% | _divideComplex, imaginary part |
| 5.9b | 3.7% | Octave 3.8, jcobi/2 |
| 2.9b | 77.8% | Octave 3.8, jcobi/1 |
| 2.9b | 2.9% | Octave 3.8, jcobi/4 |
| 2.6b | 0% | _divideComplex, real part |