| 152× | rewrite-expression-head |
442 calls:
| 58.5s | (* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)))))) |
| 51.8s | (/ (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ 4.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 12.507343278686905 (+ 5.0 (- z))) (+ (/ 1.5056327351493116e-07 (+ 8.0 (- z))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))) (exp (+ 0.5 (+ (- z) 7.0)))) |
| 45.8s | (* (* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)))))) |
| 42.7s | (+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0))) |
| 41.9s | (+ (+ (+ (+ (/ 771.3234287776531 (- 3.0 z)) (+ (/ -176.6150291621406 (- 4.0 z)) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))))) (/ 12.507343278686905 (- 5.0 z))) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (+ (/ -0.13857109526572012 (- 6.0 z)) (/ 9.984369578019572e-06 (+ (- z) 7.0))))) (/ -1259.1392167224028 (+ (- z) 2.0))) |
| 2800345× | frac-times |
| 1104589× | cbrt-div |
| 1078974× | associate-*r/ |
| 788286× | associate-*l/ |
| 746717× | flip3-- flip-- |
| 373441× | associate-/l/ |
| 13823× | *-un-lft-identity |
| 12850× | times-frac |
| 9865× | add-sqr-sqrt |
| 6766× | add-cube-cbrt |
| 4846× | sqrt-prod |
| 3326× | distribute-lft-out |
| 3018× | add-exp-log |
| 2782× | frac-add |
| 2475× | add-cbrt-cube |
| 1669× | prod-diff |
| 1642× | associate-*l* |
| 1376× | cbrt-prod |
| 1259× | pow1 |
| 1175× | flip-+ flip3-+ |
| 1166× | associate-*r* |
| 1109× | prod-exp |
| 918× | cbrt-unprod |
| 904× | add-log-exp |
| 795× | div-exp |
| 779× | unpow-prod-down |
| 678× | associate-/r* |
| 676× | difference-of-squares |
| 609× | associate-/l* |
| 597× | cbrt-undiv |
| 536× | distribute-lft-out-- cube-prod |
| 489× | unswap-sqr |
| 474× | associate-/r/ |
| 448× | log1p-expm1-u |
| 442× | expm1-log1p-u |
| 418× | div-inv |
| 343× | swap-sqr |
| 327× | pow-prod-down |
| 296× | sum-log |
| 285× | distribute-rgt-neg-in |
| 245× | sqr-pow |
| 237× | exp-sum |
| 205× | distribute-rgt-in distribute-lft-in |
| 199× | fma-def |
| 191× | exp-diff |
| 163× | fma-neg |
| 124× | *-commutative |
| 123× | log-pow |
| 103× | frac-2neg clear-num |
| 90× | fma-udef unpow3 cube-mult |
| 77× | pow-prod-up log-prod |
| 73× | pow-unpow rec-exp pow-exp 1-exp |
| 71× | associate--r+ |
| 67× | sub-neg |
| 66× | sqrt-div |
| 61× | associate--l+ |
| 56× | exp-prod |
| 55× | pow1/3 |
| 54× | pow-to-exp |
| 52× | sqrt-pow1 |
| 42× | pow1/2 diff-log |
| 32× | frac-sub |
| 30× | +-commutative |
| 29× | pow-sqr |
| 28× | distribute-lft-neg-in |
| 27× | pow-plus |
| 24× | pow-pow |
| 19× | pow2 |
| 18× | associate-+l+ |
| 16× | pow-flip |
| 15× | div-sub |
| 14× | inv-pow |
| 13× | associate-+l- |
| 12× | rem-sqrt-square |
| 11× | rem-cube-cbrt |
| 9× | log-div |
| 8× | cube-div associate-+r+ neg-mul-1 |
| 7× | un-div-inv expm1-udef |
| 6× | distribute-neg-in expm1-log1p rem-log-exp |
| 5× | hypot-def associate--l- |
| 4× | sin-sum sub-div pow-sub cos-sum |
| 3× | sqrt-undiv log1p-udef log1p-expm1 unpow-prod-up hypot-udef associate--r- distribute-rgt-out-- distribute-rgt-neg-out unpow2 |
| 2× | rem-exp-log pow3 distribute-lft-neg-out associate-+r- neg-sub0 neg-log sum-cubes distribute-neg-frac |
| 1× | difference-cubes sqrt-pow2 distribute-rgt-out |
| 99× | intervals |
| 47.9s | 15615× | body | 10240 | exit |
| 20.9s | 468966× | body | 80 | valid |
| 13.9s | 30619× | body | 1280 | valid |
| 6.3s | 22638× | body | 640 | valid |
| 2.6s | 3031× | body | 1280 | nan |
| 2.5s | 71226× | body | 80 | nan |
| 2.1s | 11975× | body | 320 | valid |
| 1.5s | 2469× | body | 640 | nan |
| 1.3s | 10186× | body | 160 | valid |
| 556.0ms | 1283× | body | 320 | nan |
| 503.0ms | 41536× | pre | 80 | true |
| 365.0ms | 1509× | body | 2560 | valid |
| 190.0ms | 649× | body | 160 | nan |
| 140.0ms | 576× | body | 5120 | valid |
442 calls:
| 891.0ms | (* (/ (sqrt (+ (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (* (pow x 4) 0.0424060604)) (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0)))) (* (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (+ (* (* x x) 0.0008327945) 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))))) (/ (sqrt (fma (pow (* x x) 4) (fma 0.0001789971 (* x x) 0.0005064034) (fma (pow x 4) 0.0424060604 (fma (pow x 6) 0.0072644182 (fma (* x x) 0.1049934947 1.0))))) (/ (cbrt (fma (* 2.0 0.0001789971) (pow (* x x) 6) (fma (pow (* x x) 4) (fma (* x x) 0.0008327945 0.0140005442) (fma 0.0694555761 (pow x 6) (fma 0.2909738639 (pow x 4) (fma (* x x) 0.7715471019 1.0)))))) x))) |
| 858.0ms | (* (* (- (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2)))) (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) -0.284496736) 0.254829592) (exp (pow (fabs x) 2))) (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.0)) |
| 838.0ms | (/ (/ (* (* 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)) |
| 725.0ms | (* (* (/ (* (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))) (+ (+ (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (+ (/ -176.6150291621406 (+ (- z 1.0) 4.0)) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ 676.5203681218851 z) (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) 0.9999999999998099)))))) |
| 718.0ms | (expm1 (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))) |
Total 30.8b remaining (30.3%)
Threshold costs 6.0b (5.9%)
| 10.4b | 27.5% | _divideComplex, real part |
| 7.9b | 31.9% | _divideComplex, imaginary part |
| 2.9b | 77.4% | Octave 3.8, jcobi/1 |
| 2.0b | 0% | Jmat.Real.lambertw, newton loop step |
| 1.6b | 35.5% | Octave 3.8, jcobi/3 |