| 96× | intervals |
| 6.9m | 107018× | body | 10240 | exit |
| 1.3m | 419088× | body | 80 | valid |
| 33.7s | 26442× | body | 1280 | valid |
| 18.9s | 20592× | body | 640 | valid |
| 12.1s | 70130× | body | 80 | nan |
| 10.4s | 3089× | body | 1280 | nan |
| 6.9s | 2598× | body | 640 | nan |
| 6.8s | 10795× | body | 320 | valid |
| 3.4s | 9654× | body | 160 | valid |
| 3.2s | 49536× | pre | 80 | true |
| 2.2s | 1320× | body | 320 | nan |
| 1.8s | 1456× | body | 2560 | valid |
| 692.0ms | 601× | body | 5120 | valid |
| 653.0ms | 694× | body | 160 | nan |
496 calls:
| 2.9m | (- (pow (pow 1 3) 3) (pow (* (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3)) (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3))) 3)) |
| 4.6s | (- (pow 1 3) (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3)) |
| 4.0s | (- (pow 1 3) (* (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3)) (sqrt (pow (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) 3)))) |
| 3.2s | (+ (* (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))) (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911))))) (* 1 (/ (+ 0.254829592 (/ (+ (/ (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911))) -0.284496736) (+ 1 (* (fabs x) 0.3275911)))) (* (exp (* (fabs x) (fabs x))) (+ 1 (* (fabs x) 0.3275911)))))) |
| 3.2s | (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0)))) |
| 154× | rewrite-expression-head |
496 calls:
| 24.4s | (* (* (/ 1 (sqrt (* (cbrt (exp (+ (+ 7 (- z 1)) 0.5))) (cbrt (exp (+ (+ 7 (- z 1)) 0.5)))))) (* (/ (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (cbrt (exp (+ (+ 7 (- z 1)) 0.5))))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5)))))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z))))) |
| 18.1s | (* (/ (* (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (* PI 2))) (exp (+ (+ 7 (- z 1)) 0.5))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z))))) |
| 17.6s | (* (* (/ (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5)))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5))))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z))))) |
| 16.7s | (* (* 1 (* (/ (pow (+ (+ 7 (- z 1)) 0.5) (+ (- z 1) 0.5)) (sqrt (cbrt (exp (+ (+ 7 (- z 1)) 0.5))))) (/ (sqrt (* PI 2)) (sqrt (exp (+ (+ 7 (- z 1)) 0.5)))))) (+ (+ (/ -0.13857109526572012 (+ z 5)) (+ (/ 12.507343278686905 (+ z 4)) (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ 7 z))))) (+ (+ (/ -176.6150291621406 (+ (- z 1) 4)) (+ 0.9999999999998099 (+ (/ 676.5203681218851 z) (/ 771.3234287776531 (+ 2 z))))) (/ -1259.1392167224028 (+ 1 z))))) |
| 9.6s | (* (/ (+ (* (- (* (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971))))) (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971)))))) (* 1 1)) (- (* (* (* x x) (* x x)) 0.0072644182) 0.1049934947)) (* (- (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971))))) 1) (* (* x x) (- (* (* (* (* x x) (* x x)) 0.0072644182) (* (* (* x x) (* x x)) 0.0072644182)) (* 0.1049934947 0.1049934947))))) (* (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (+ (* 0.0001789971 (* 2 (* (* x x) (* x x)))) (+ 0.0140005442 (* 0.0008327945 (* x x))))) (+ (* (* x x) (+ 0.7715471019 (* 0.0694555761 (* (* x x) (* x x))))) (+ 1 (* 0.2909738639 (* (* x x) (* x x)))))) (* (- (* (* (* x x) (* x x)) (+ 0.0424060604 (* (* (* x x) (* x x)) (+ 0.0005064034 (* (* x x) 0.0001789971))))) 1) (- (* (* (* x x) (* x x)) 0.0072644182) 0.1049934947)))) x) |
| 12448× | *-un-lft-identity |
| 9793× | times-frac |
| 6688× | add-sqr-sqrt |
| 4835× | add-cube-cbrt |
| 4251× | distribute-lft-out |
| 3419× | pow1 |
| 3000× | frac-add |
| 2995× | add-exp-log |
| 2367× | add-cbrt-cube |
| 1899× | associate-*l* |
| 1843× | frac-times |
| 1785× | flip-+ flip3-+ |
| 1714× | associate-*r* |
| 1546× | associate-*r/ |
| 1270× | sqrt-prod |
| 1194× | prod-exp |
| 973× | pow-prod-up |
| 923× | associate-*l/ |
| 919× | cbrt-prod |
| 896× | associate-/r/ |
| 887× | cbrt-unprod |
| 760× | add-log-exp |
| 753× | pow-prod-down |
| 654× | div-exp |
| 565× | associate-/l* |
| 560× | cbrt-div |
| 530× | pow-plus |
| 524× | sqrt-div |
| 496× | insert-posit16 |
| 490× | flip3-- flip-- |
| 465× | difference-of-squares |
| 454× | cbrt-undiv |
| 403× | associate-/r* |
| 397× | unpow-prod-down |
| 383× | unswap-sqr |
| 367× | div-inv |
| 320× | pow-sqr |
| 283× | distribute-lft-out-- |
| 231× | swap-sqr |
| 206× | pow2 |
| 185× | associate-/l/ |
| 180× | *-commutative |
| 153× | sqrt-pow1 |
| 151× | pow1/3 |
| 135× | sqr-pow |
| 134× | cube-prod |
| 117× | log-pow |
| 93× | pow1/2 |
| 88× | pow-exp |
| 87× | frac-2neg clear-num |
| 76× | exp-sum |
| 75× | sub-neg |
| 72× | diff-log |
| 71× | sum-log |
| 67× | 1-exp |
| 62× | log-prod distribute-rgt-in distribute-lft-in |
| 58× | rem-sqrt-square |
| 57× | pow-to-exp |
| 46× | rec-exp +-commutative |
| 37× | pow-unpow |
| 36× | associate--l+ |
| 33× | unpow-prod-up |
| 31× | pow3 |
| 29× | distribute-rgt-out |
| 28× | distribute-rgt1-in |
| 27× | cube-unmult |
| 23× | associate-+l- |
| 22× | frac-sub exp-prod |
| 19× | exp-diff associate-+r- |
| 18× | rem-cube-cbrt div-sub |
| 15× | pow-flip pow-pow |
| 11× | associate--l- |
| 10× | difference-of-sqr-1 |
| 9× | associate-+l+ inv-pow rem-exp-log log-div |
| 8× | associate--r+ |
| 7× | un-div-inv cube-mult |
| 6× | sin-sum associate-+r+ unpow3 cube-div |
| 5× | pow-sub |
| 4× | rem-log-exp |
| 3× | sqrt-undiv exp-to-pow |
| 2× | remove-posit16 sub0-neg sqrt-unprod difference-cubes unpow1/3 associate--r- |
| 1× | rem-square-sqrt cos-sum rem-cbrt-cube unsub-neg |
Total 92.4b remaining (36.6%)
Threshold costs 3.8b (1.5%)
| 10.6b | 50.4% | math.log/2 on complex, real part |
| 10.3b | 56.6% | math.log10 on complex, real part |
| 10.1b | 57.2% | math.log/1 on complex, real part |
| 8.9b | 59.4% | math.abs on complex |
| 8.8b | 42.2% | Octave 3.8, jcobi/4 |