25601 calls:
| 2.1s | (/ (* (* (* (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))))) |
| 2.0s | (* (/ (* (* 1 1) 1) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (* (+ (+ (/ 3/4 (pow (fabs x) 5)) (+ (/ 15/8 (pow (fabs x) 7)) (/ 1 (fabs x)))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x))))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (+ (/ 15/8 (pow (fabs x) 7)) (/ 1 (fabs x)))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))))) (+ (+ (/ 3/4 (pow (fabs x) 5)) (+ (/ 15/8 (pow (fabs x) 7)) (/ 1 (fabs x)))) (/ 1/2 (* (fabs x) (* (fabs x) (fabs x)))))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))))) |
| 1.9s | (* (+ (* (* x.re x.re) (* x.re x.re)) (+ (* (* x.im x.im) (* x.im x.im)) (* (* x.re x.re) (* x.im x.im)))) (- (* x.re x.im) (* x.im x.re))) |
| 1.8s | (* (* (* (/ 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 (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 (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)))))) |
| 1.8s | (/ (* (* (* (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))))) |
| 89× | intervals |
| 6.9m | 105171× | body | 10240 | exit |
| 1.1m | 391979× | body | 80 | valid |
| 37.9s | 26209× | body | 1280 | valid |
| 20.7s | 20163× | body | 640 | valid |
| 11.9s | 3151× | body | 1280 | nan |
| 11.7s | 69452× | body | 80 | nan |
| 8.3s | 2565× | body | 640 | nan |
| 6.2s | 10039× | body | 320 | valid |
| 4.9s | 9361× | body | 160 | valid |
| 3.1s | 1248× | body | 320 | nan |
| 1.5s | 33536× | pre | 80 | true |
| 1.4s | 1454× | body | 2560 | valid |
| 1.2s | 674× | body | 160 | nan |
| 1.0s | 592× | body | 5120 | valid |
| 139× | rewrite-expression-head |
412 calls:
| 36.7s | (* (+ (/ 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))))) |
| 9.0s | (cbrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) |
| 9.0s | (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) |
| 8.8s | (cbrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) |
| 8.8s | (cbrt (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) |
| 28783× | *-un-lft-identity |
| 28620× | times-frac |
| 15195× | add-sqr-sqrt |
| 11837× | add-cube-cbrt |
| 9008× | distribute-lft-out |
| 5608× | sqrt-prod |
| 4038× | pow1 |
| 2278× | add-exp-log |
| 2157× | prod-diff |
| 1698× | add-cbrt-cube |
| 1689× | fma-def |
| 1644× | associate-*r* |
| 1388× | pow-prod-up |
| 1181× | associate-*l* |
| 1068× | difference-of-squares |
| 983× | div-inv |
| 876× | associate-/r/ |
| 833× | prod-exp |
| 822× | distribute-lft-out-- |
| 788× | log-pow |
| 746× | associate-/l* |
| 634× | add-log-exp |
| 616× | associate-/r* |
| 608× | pow-plus |
| 599× | flip-+ flip3-+ |
| 572× | pow-prod-down |
| 553× | cbrt-unprod |
| 507× | div-exp |
| 412× | expm1-log1p-u insert-posit16 log1p-expm1-u |
| 402× | associate-*r/ |
| 398× | flip3-- flip-- |
| 346× | frac-times |
| 320× | unswap-sqr |
| 314× | frac-add |
| 311× | pow-sqr |
| 296× | cbrt-undiv |
| 290× | associate-*l/ |
| 240× | distribute-rgt-in distribute-lft-in |
| 227× | frac-sub |
| 224× | pow2 |
| 201× | sqrt-pow1 |
| 190× | swap-sqr |
| 184× | fma-neg |
| 151× | sqrt-div |
| 140× | associate-/l/ |
| 134× | unpow-prod-down |
| 130× | *-commutative |
| 124× | exp-prod |
| 120× | pow1/2 |
| 118× | exp-sum |
| 99× | associate--r+ |
| 92× | pow-exp |
| 90× | sum-log |
| 89× | frac-2neg clear-num |
| 87× | cbrt-prod |
| 75× | associate--l+ |
| 71× | 1-exp |
| 70× | log-prod |
| 69× | sub-neg |
| 66× | rec-exp |
| 65× | sqr-pow |
| 55× | fma-udef |
| 53× | pow-to-exp |
| 52× | cube-unmult |
| 48× | associate-+l- pow-sub |
| 41× | +-commutative rem-sqrt-square |
| 40× | associate-+l+ |
| 39× | exp-neg |
| 37× | diff-log |
| 36× | pow-unpow |
| 33× | pow1/3 |
| 32× | exp-diff pow-div |
| 30× | pow-flip |
| 26× | neg-sub0 |
| 25× | distribute-rgt1-in inv-pow |
| 22× | distribute-rgt-out |
| 21× | unpow-prod-up |
| 18× | cube-prod |
| 17× | log-div |
| 16× | un-div-inv |
| 14× | div-sub |
| 10× | sin-sum associate-+r+ hypot-def |
| 9× | pow-pow |
| 7× | sqrt-unprod |
| 6× | distribute-lft1-in unpow3 rem-log-exp exp-to-pow cube-mult |
| 5× | rem-square-sqrt |
| 4× | associate-+r- pow3 sub-div associate--r- |
| 3× | cbrt-div |
| 2× | distribute-rgt-out-- rem-exp-log cos-sum |
| 1× | associate--l- e-exp-1 |
412 calls:
| 2.2s | (- (* 1 1) (* (/ (* (+ (+ (/ 1.061405429 (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))) (fma (+ (/ 1.453152027 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 0.284496736) (/ -1 (fma 0.3275911 (fabs x) 1)) (/ 1.421413741 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) 0.254829592) (/ -1 (fma 0.3275911 (fabs x) 1))) (exp (* (fabs x) (fabs x)))) (/ (* (+ (+ (/ 1.061405429 (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)))) (fma (+ (/ 1.453152027 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 0.284496736) (/ -1 (fma 0.3275911 (fabs x) 1)) (/ 1.421413741 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))) 0.254829592) (/ -1 (fma 0.3275911 (fabs x) 1))) (exp (* (fabs x) (fabs x)))))) |
| 1.5s | (* (sqrt (/ (/ (fma (+ (+ alpha beta) i) i (* beta alpha)) (fma 2 i (+ alpha beta))) (+ (fma 2 i (+ alpha beta)) (sqrt 1.0)))) (/ (/ (* (+ (+ alpha beta) i) i) (fma 2 i (+ alpha beta))) (- (fma 2 i (+ alpha beta)) (sqrt 1.0)))) |
| 1.2s | (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (+ (- (/ 1.421413741 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) (* (/ 1 (fma 0.3275911 (fabs x) 1)) (+ (/ 1.453152027 (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))) 0.284496736))) (/ 1.061405429 (* (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1)) (* (fma 0.3275911 (fabs x) 1) (fma 0.3275911 (fabs x) 1))))))) (exp (- (* (fabs x) (fabs x)))))) |
| 1.1s | (* (* (pow (* -2 (log u1)) (/ 0.5 2)) (pow (* -2 (log u1)) (/ 0.5 2))) 1/6) |
| 1.0s | (- 1 (* (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1 (+ 1 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 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)))))) |
Total 21.3b remaining (19.1%)
Threshold costs 5.7b (5.1%)
| 7.2b | 33.7% | _divideComplex, real part |
| 6.8b | 37.6% | _divideComplex, imaginary part |
| 1.6b | 44.8% | Octave 3.8, jcobi/4 |
| 0.6b | 65.8% | Jmat.Real.lambertw, newton loop step |
| 0.6b | 0% | math.cos on complex, imaginary part |