10990 calls:
| 2.7s | (/ (/ (* (* (* (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))) |
| 2.4s | (* 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)))) |
| 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))))) (* (* (- (* (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))) |
| 1.7s | (* 1 (* (* (pow (+ (- z -6) 0.5) z) (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)))) |
| 1.5s | (* (+ (* (* 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))) |
| 89× | intervals |
| 6.4m | 99874× | body | 10240 | exit |
| 1.2m | 398799× | body | 80 | valid |
| 24.9s | 22562× | body | 1280 | valid |
| 13.2s | 18431× | body | 640 | valid |
| 12.9s | 70534× | body | 80 | nan |
| 5.6s | 1584× | body | 1280 | nan |
| 4.7s | 9479× | body | 320 | valid |
| 4.1s | 1334× | body | 640 | nan |
| 3.9s | 8897× | body | 160 | valid |
| 1.8s | 41536× | pre | 80 | true |
| 1.3s | 650× | body | 320 | nan |
| 1.1s | 1351× | body | 2560 | valid |
| 588.0ms | 596× | body | 5120 | valid |
| 418.0ms | 345× | body | 160 | nan |
415 calls:
| 1.2s | (log (exp (- 1 (/ (/ (fma (/ (* (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))))) (* (cbrt (fma 0.3275911 (fabs x) 1)) (cbrt (fma 0.3275911 (fabs x) 1)))) (/ (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (fma 0.3275911 (fabs x) 1))) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))))) |
| 1.2s | (- 1 (/ (/ (fma (/ (* (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))))) (* (cbrt (fma 0.3275911 (fabs x) 1)) (cbrt (fma 0.3275911 (fabs x) 1)))) (/ (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (fma 0.3275911 (fabs x) 1))) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))) |
| 1.2s | (* 1/6 (cbrt (pow (* (* (* -2 (log u1)) (* -2 (log u1))) (* -2 (log u1))) 0.5))) |
| 1.2s | (- 1 (/ (/ (fma (/ (* (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))))) (* (cbrt (fma 0.3275911 (fabs x) 1)) (cbrt (fma 0.3275911 (fabs x) 1)))) (/ (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (fma 0.3275911 (fabs x) 1))) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))) |
| 1.2s | (- 1 (/ (/ (fma (/ (* (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1))))) (* (cbrt (fma 0.3275911 (fabs x) 1)) (cbrt (fma 0.3275911 (fabs x) 1)))) (/ (cbrt (+ -0.284496736 (/ (+ (/ (+ (/ 1.061405429 (fma 0.3275911 (fabs x) 1)) -1.453152027) (fma 0.3275911 (fabs x) 1)) 1.421413741) (fma 0.3275911 (fabs x) 1)))) (cbrt (fma 0.3275911 (fabs x) 1))) 0.254829592) (fma 0.3275911 (fabs x) 1)) (exp (* (fabs x) (fabs x))))) |
| 142× | rewrite-expression-head |
415 calls:
| 2.5s | (* (/ (+ (+ (+ (+ (+ 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) |
| 2.5s | (/ (+ (+ (+ (+ (+ 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))))) |
| 2.3s | (/ (* (+ (+ (+ (+ (+ 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)))) 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))))) |
| 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)))))) |
| 1.4s | (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))) |
| 47214× | times-frac |
| 19030× | *-un-lft-identity |
| 19014× | add-sqr-sqrt |
| 18972× | add-cube-cbrt |
| 17660× | sqrt-prod |
| 4213× | frac-add |
| 3272× | flip-+ flip3-+ |
| 3028× | associate-/r/ |
| 1859× | div-inv |
| 1546× | frac-times |
| 1519× | associate-*r/ |
| 1270× | add-exp-log |
| 1193× | pow1 |
| 1055× | add-cbrt-cube |
| 1032× | associate-*l/ |
| 673× | associate-/r* |
| 522× | associate-+l- |
| 518× | pow-sub |
| 515× | add-log-exp |
| 465× | associate-/l* |
| 438× | associate-*l* |
| 425× | associate-/l/ |
| 415× | expm1-log1p-u insert-posit16 log1p-expm1-u |
| 374× | flip3-- flip-- |
| 366× | cbrt-div |
| 363× | associate-*r* |
| 353× | prod-exp |
| 295× | log-pow |
| 264× | exp-diff |
| 258× | neg-sub0 exp-neg |
| 250× | cbrt-unprod |
| 249× | prod-diff |
| 229× | pow-prod-down |
| 219× | div-exp |
| 168× | cbrt-undiv |
| 154× | sqrt-div |
| 141× | fma-def |
| 125× | *-commutative |
| 123× | distribute-rgt-in distribute-lft-in |
| 117× | cbrt-prod |
| 98× | frac-2neg clear-num |
| 85× | pow-prod-up |
| 83× | pow1/3 |
| 81× | fma-neg |
| 79× | sub-neg |
| 63× | rec-exp |
| 62× | associate-+r+ |
| 60× | pow-plus |
| 57× | pow2 |
| 55× | unpow3 cube-mult |
| 51× | fma-udef |
| 48× | unpow-prod-down |
| 45× | log-prod |
| 43× | pow1/2 |
| 40× | pow-exp pow-to-exp |
| 36× | pow-div +-commutative |
| 35× | pow-flip sum-log |
| 34× | exp-sum |
| 31× | inv-pow |
| 22× | frac-sub |
| 21× | difference-of-squares |
| 19× | distribute-lft-out diff-log |
| 16× | div-sub |
| 15× | associate-+l+ cube-prod distribute-lft-out-- exp-prod |
| 14× | distribute-rgt-out |
| 13× | associate--l+ rem-sqrt-square |
| 12× | sin-sum |
| 11× | distribute-rgt1-in |
| 9× | pow3 |
| 7× | rem-log-exp |
| 6× | difference-cubes hypot-def |
| 5× | associate--l- sqrt-unprod associate--r+ log-div |
| 4× | cube-unmult difference-of-sqr-1 distribute-rgt-neg-in un-div-inv hypot-udef expm1-def distribute-lft-neg-in |
| 2× | associate-+r- distribute-lft1-in unpow-prod-up remove-double-div distribute-neg-frac rem-square-sqrt rem-cbrt-cube |
| 1× | distribute-lft-neg-out neg-mul-1 pow-pow rem-exp-log cos-sum distribute-neg-in associate--r- |
Total 29.9b remaining (23.5%)
| 7.0b | 36.2% | _divideComplex, imaginary part |
| 6.8b | 35% | _divideComplex, real part |
| 5.4b | 17% | Octave 3.8, jcobi/2 |
| 3.1b | 75.4% | Octave 3.8, jcobi/1 |
| 1.5b | 0% | Jmat.Real.lambertw, newton loop step |