| 153× | rewrite-expression-head |
446 calls:
| 3.5m | (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))) |
| 2.0m | (* (* (/ (cbrt (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (* (* PI 2.0) (sqrt (* PI 2.0))))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))) |
| 2.0m | (* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))) |
| 53.6s | (* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))))) |
| 35.4s | (+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ (- z) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z))))))) |
| 1655357× | frac-times |
| 1295974× | associate-*l/ |
| 876704× | associate-*r/ |
| 789555× | frac-add |
| 20212× | times-frac |
| 18270× | flip-+ flip3-+ |
| 16088× | *-un-lft-identity |
| 12621× | add-sqr-sqrt |
| 10190× | add-cube-cbrt |
| 5339× | sqrt-prod |
| 3259× | distribute-rgt-neg-in |
| 3241× | distribute-lft-neg-in |
| 2845× | distribute-lft-out |
| 2075× | add-exp-log |
| 1640× | add-cbrt-cube |
| 1396× | associate-*l* |
| 1250× | pow1 |
| 1114× | prod-diff |
| 1074× | associate-*r* |
| 802× | associate-/l* |
| 736× | add-log-exp |
| 689× | div-inv |
| 639× | prod-exp |
| 621× | difference-of-squares |
| 493× | div-exp |
| 475× | exp-diff |
| 466× | neg-mul-1 |
| 461× | associate-/r* |
| 447× | log1p-expm1-u |
| 446× | expm1-log1p-u |
| 429× | cbrt-unprod |
| 369× | distribute-lft-out-- |
| 356× | cbrt-prod |
| 348× | cbrt-undiv |
| 333× | unswap-sqr |
| 298× | unpow-prod-down |
| 292× | associate-/r/ |
| 285× | pow-prod-down |
| 242× | swap-sqr |
| 215× | fma-def |
| 184× | cube-prod |
| 163× | sum-log |
| 153× | fma-neg |
| 151× | exp-sum |
| 148× | log-pow |
| 133× | *-commutative |
| 128× | distribute-rgt-in distribute-lft-in |
| 119× | flip3-- flip-- |
| 111× | sqrt-pow1 |
| 96× | pow1/3 sqrt-div |
| 92× | clear-num frac-2neg |
| 91× | sqr-pow pow-exp |
| 89× | associate-/l/ |
| 78× | log-prod |
| 75× | fma-udef |
| 71× | pow1/2 |
| 70× | associate--r+ |
| 68× | pow-unpow |
| 64× | pow-prod-up |
| 61× | pow-to-exp cbrt-div |
| 59× | associate--l+ |
| 56× | exp-prod sub-neg |
| 46× | associate-+l+ |
| 45× | pow-sqr |
| 41× | rec-exp 1-exp diff-log |
| 29× | pow-plus |
| 28× | rem-sqrt-square |
| 27× | unpow3 cube-mult |
| 25× | pow2 |
| 23× | +-commutative |
| 21× | pow-pow |
| 17× | div-sub |
| 13× | rem-cube-cbrt |
| 12× | associate-+l- |
| 11× | frac-sub |
| 8× | rem-log-exp log-div |
| 7× | cos-sum distribute-neg-frac |
| 6× | cube-div unpow-prod-up sqrt-undiv |
| 5× | log1p-udef sqrt-unprod log1p-expm1 expm1-log1p pow-flip expm1-udef associate--l- |
| 4× | rem-exp-log un-div-inv sin-sum distribute-neg-in pow-sub associate-+r+ rem-square-sqrt |
| 3× | inv-pow unpow2 hypot-udef distribute-frac-neg distribute-rgt-neg-out rem-cbrt-cube |
| 2× | sqrt-pow2 distribute-lft-neg-out neg-sub0 hypot-def associate--r- |
| 1× | pow3 distribute-rgt-out |
| 98× | intervals |
| 1.2m | 12136× | body | 10240 | exit |
| 50.4s | 437645× | body | 80 | valid |
| 27.3s | 26654× | body | 1280 | valid |
| 12.9s | 21309× | body | 640 | valid |
| 6.5s | 68580× | body | 80 | nan |
| 4.6s | 1635× | body | 1280 | nan |
| 3.9s | 10483× | body | 320 | valid |
| 3.3s | 9401× | body | 160 | valid |
| 2.4s | 1328× | body | 640 | nan |
| 2.3s | 49536× | pre | 80 | true |
| 849.0ms | 1515× | body | 2560 | valid |
| 759.0ms | 660× | body | 320 | nan |
| 664.0ms | 315× | body | 160 | nan |
| 318.0ms | 599× | body | 5120 | valid |
444 calls:
| 3.7s | (/ (* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))) |
| 3.6s | (* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))) |
| 1.6s | (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0)) |
| 1.4s | (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) |
| 1.3s | (* (* (/ (cbrt (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (* (* PI 2.0) (sqrt (* PI 2.0))))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))) |
Total 31.8b remaining (23.2%)
Threshold costs 5.5b (4%)
| 10.2b | 25.7% | _divideComplex, imaginary part |
| 7.7b | 32.2% | _divideComplex, real part |
| 3.0b | 77.3% | Octave 3.8, jcobi/1 |
| 2.3b | 39.9% | Octave 3.8, jcobi/4 |
| 2.1b | 18.6% | Octave 3.8, jcobi/3 |