17857 calls:
| 2.4s | (/ (* (* (* (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))))) |
| 2.2s | (* (/ (* (/ (* (* 1 1) 1) (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))) (/ (* (* (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (/ 1 (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))))) |
| 2.1s | (* (/ (* (/ (* (* 1 1) 1) (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x))))) (/ (* (* (* (/ 1 (fma 0.3275911 (fabs x) 1)) (/ 1 (fma 0.3275911 (fabs x) 1))) (/ 1 (fma 0.3275911 (fabs x) 1))) (* (* (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))))) |
| 1.8s | (/ (* (* (* (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma (+ (+ alpha beta) i) i (* beta alpha))) (fma (+ (+ alpha beta) i) i (* beta alpha))) (* (* (* (+ (+ alpha beta) i) i) (* (+ (+ alpha beta) i) i)) (* (+ (+ 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))))) |
| 1.8s | (/ (* (* (* (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))))) |
| 89× | intervals |
| 6.8m | 103330× | body | 10240 | exit |
| 1.2m | 394817× | body | 80 | valid |
| 39.0s | 26142× | body | 1280 | valid |
| 19.9s | 20952× | body | 640 | valid |
| 11.4s | 3138× | body | 1280 | nan |
| 11.1s | 69415× | body | 80 | nan |
| 7.9s | 10679× | body | 320 | valid |
| 7.1s | 2651× | body | 640 | nan |
| 3.2s | 1320× | body | 320 | nan |
| 2.5s | 5468× | body | 160 | valid |
| 2.2s | 41536× | pre | 80 | true |
| 1.2s | 1406× | body | 2560 | valid |
| 839.0ms | 630× | body | 160 | nan |
| 662.0ms | 630× | body | 5120 | valid |
| 142× | rewrite-expression-head |
451 calls:
| 37.2s | (* (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5)))) (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5))))) |
| 29.6s | (* (* (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (- (+ (+ 7 (- z 1)) 0.5)))) (+ (/ 12.507343278686905 (+ z 4)) (+ (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))) (/ -0.13857109526572012 (- z -5))))) |
| 16.2s | (* (/ (+ (+ (+ (+ (+ 1 (* (* x x) 0.1049934947)) (* 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) |
| 16.0s | (* (/ (+ (+ (+ (+ (+ 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) |
| 9.1s | (/ (+ (+ (+ (+ (+ 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))))) |
| 14355× | *-un-lft-identity |
| 9186× | times-frac |
| 6428× | add-sqr-sqrt |
| 5171× | add-cube-cbrt |
| 4352× | distribute-lft-out |
| 3018× | pow1 |
| 2884× | add-exp-log |
| 1846× | sqrt-prod |
| 1836× | add-cbrt-cube |
| 1653× | prod-diff |
| 1183× | prod-exp |
| 1140× | pow-prod-up |
| 977× | distribute-lft-out-- |
| 880× | associate-*l* |
| 834× | div-exp |
| 718× | associate-*r* |
| 676× | add-log-exp |
| 647× | associate-*l/ |
| 622× | sqrt-pow1 |
| 621× | unpow-prod-down |
| 613× | associate-/l* |
| 571× | cbrt-unprod |
| 567× | frac-times |
| 561× | frac-add |
| 527× | flip-+ flip3-+ |
| 522× | pow-prod-down |
| 509× | cube-prod |
| 494× | pow-plus |
| 474× | associate-/r* |
| 451× | expm1-log1p-u log1p-expm1-u insert-posit16 |
| 440× | div-inv |
| 427× | distribute-rgt-in distribute-lft-in |
| 365× | cbrt-div |
| 353× | cbrt-prod |
| 351× | cbrt-undiv |
| 343× | pow1/2 |
| 327× | associate-/r/ |
| 323× | difference-of-squares |
| 311× | associate-*r/ |
| 310× | pow-sqr |
| 308× | pow-exp |
| 288× | unswap-sqr |
| 275× | flip3-- flip-- |
| 236× | swap-sqr |
| 228× | fma-def |
| 193× | 1-exp rec-exp |
| 188× | sqr-pow |
| 183× | fma-neg |
| 167× | pow2 |
| 142× | *-commutative |
| 138× | exp-sum |
| 133× | pow-to-exp |
| 125× | log-pow |
| 99× | cube-mult |
| 98× | unpow3 |
| 94× | associate-/l/ |
| 93× | sum-log log-prod frac-2neg clear-num |
| 90× | pow1/3 |
| 88× | sqrt-div |
| 85× | associate-+l- |
| 82× | pow-sub |
| 79× | exp-neg |
| 75× | distribute-rgt-out |
| 69× | sub-neg |
| 65× | fma-udef |
| 54× | exp-diff |
| 53× | neg-sub0 |
| 41× | exp-prod |
| 40× | diff-log |
| 39× | cube-unmult |
| 34× | un-div-inv |
| 32× | distribute-rgt1-in pow-div |
| 29× | pow-flip +-commutative |
| 27× | pow-unpow |
| 25× | inv-pow |
| 24× | rem-cube-cbrt frac-sub rem-sqrt-square |
| 19× | sqrt-unprod |
| 18× | associate-+l+ div-sub |
| 17× | hypot-udef |
| 12× | pow-pow |
| 11× | sin-sum associate--l+ |
| 10× | pow3 hypot-def |
| 8× | sum-cubes |
| 7× | rem-square-sqrt |
| 6× | rem-exp-log cube-div |
| 5× | associate-+r+ rem-log-exp exp-to-pow |
| 4× | unpow-prod-up sqrt-undiv associate--r+ |
| 3× | log-div |
| 2× | distribute-lft1-in difference-cubes rem-cbrt-cube associate--r- |
| 1× | expm1-log1p expm1-udef associate--l- cos-sum sin-mult |
447 calls:
| 1.3s | (pow (* (pow (log u1) 1.0) (pow -2 1.0)) 0.5) |
| 1.1s | (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) |
| 1.1s | (/ 1 (* (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5) 6)) |
| 1.1s | (+ (* (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x)))) (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x))))) (* 1 (/ (* (/ 1 (fma 0.3275911 (fabs x) 1)) (fma (fma (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) -0.284496736) (/ 1 (fma 0.3275911 (fabs x) 1)) 0.254829592)) (exp (* (fabs x) (fabs x)))))) |
| 1.1s | (* (pow (/ 1 (* (pow -2 1.0) (pow (log u1) 1.0))) 0.5) 6) |
Total 27.9b remaining (24.5%)
| 10.7b | 25% | _divideComplex, real part |
| 5.6b | 10.1% | Octave 3.8, jcobi/2 |
| 3.2b | 0% | _divideComplex, imaginary part |
| 2.3b | 20.4% | Octave 3.8, jcobi/4 |
| 0.7b | 62.3% | Jmat.Real.lambertw, newton loop step |