| 166× | rewrite-expression-head |
529 calls:
| 2.3m | (* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI))) |
| 2.0m | (* (* (+ (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) 0.9999999999998099) (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (- (+ z 4.0) 1.0)))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ 1.5056327351493116e-07 (+ 8.0 (- z 1.0))))) (pow (+ (+ 7.0 (- z 1.0)) 0.5) (- z (- 1.0 0.5)))) (/ (sqrt (* PI 2.0)) (exp (+ (+ 7.0 (- z 1.0)) 0.5)))) |
| 1.6m | (* (+ (+ (+ (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (- z)))) (/ 771.3234287776531 (+ 3.0 (- z)))) 0.9999999999998099) (/ 12.507343278686905 (+ (- z) 5.0))) (+ (/ -176.6150291621406 (+ (- z) 4.0)) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))) (/ 9.984369578019572e-06 (+ 7.0 (- z)))))) (sqrt (* 2.0 PI))) |
| 1.5m | (* (+ (+ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) 0.9999999999998099) (+ (+ (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (- (+ z 4.0) 1.0)))) (+ (+ (/ -0.13857109526572012 (+ (- z 1.0) 6.0)) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ 1.5056327351493116e-07 (+ 8.0 (- z 1.0))))) (pow (+ (+ 7.0 (- z 1.0)) 0.5) (- z (- 1.0 0.5)))) |
| 23.8s | (* (+ (+ (+ (/ -0.13857109526572012 (- 6.0 z)) (+ (/ 1.5056327351493116e-07 (- 8.0 z)) (/ 9.984369578019572e-06 (- 7.0 z)))) (/ -176.6150291621406 (+ (- z) 4.0))) (+ (+ (+ (/ -1259.1392167224028 (- 2.0 z)) (/ 676.5203681218851 (- 1.0 z))) (+ 0.9999999999998099 (/ 771.3234287776531 (- 3.0 z)))) (/ 12.507343278686905 (+ 5.0 (- z))))) (sqrt (* 2.0 PI))) |
| 54478× | times-frac |
| 38630× | *-un-lft-identity |
| 24149× | add-sqr-sqrt |
| 21055× | add-cube-cbrt |
| 9048× | distribute-lft-out |
| 8213× | sqrt-prod |
| 5079× | add-exp-log |
| 4913× | frac-add |
| 4325× | frac-times |
| 4065× | associate-*l/ |
| 3193× | flip-+ flip3-+ |
| 2788× | div-exp |
| 2750× | flip3-- flip-- |
| 2572× | associate-*r* |
| 2238× | add-cbrt-cube |
| 2143× | div-inv |
| 2063× | associate-*l* |
| 1920× | swap-sqr |
| 1638× | associate-/r/ |
| 1636× | associate-*r/ |
| 1569× | pow1 |
| 1485× | associate-/l* |
| 1199× | prod-exp |
| 845× | add-log-exp |
| 825× | unpow-prod-down |
| 679× | associate-/r* |
| 627× | cbrt-undiv |
| 563× | unswap-sqr |
| 555× | cbrt-unprod |
| 548× | 1-exp |
| 503× | cbrt-prod |
| 495× | distribute-lft-out-- |
| 380× | pow-prod-down |
| 376× | cube-prod |
| 365× | difference-of-squares |
| 345× | rec-exp |
| 313× | cbrt-div |
| 296× | sqrt-div |
| 292× | sqrt-pow1 |
| 253× | pow-sub |
| 212× | log-pow |
| 183× | log-prod |
| 174× | pow-exp |
| 150× | associate-/l/ |
| 147× | sqr-pow |
| 138× | *-commutative |
| 135× | pow-unpow |
| 130× | sum-log |
| 124× | pow1/2 |
| 113× | distribute-rgt-neg-in |
| 112× | pow1/3 |
| 108× | distribute-lft-neg-in |
| 102× | pow-to-exp |
| 99× | frac-2neg clear-num |
| 96× | distribute-rgt-in distribute-lft-in |
| 76× | sub-neg |
| 68× | pow-prod-up exp-prod |
| 63× | exp-sum +-commutative |
| 60× | rem-sqrt-square |
| 53× | diff-log |
| 49× | pow-pow |
| 48× | cube-div |
| 44× | pow-sqr |
| 42× | unpow3 cube-mult |
| 37× | frac-sub |
| 30× | exp-diff |
| 27× | neg-mul-1 |
| 26× | rem-cube-cbrt |
| 24× | pow-plus |
| 23× | associate-+r+ |
| 22× | div-sub |
| 19× | associate--l+ rem-log-exp |
| 17× | associate-+l+ pow2 |
| 15× | log-div |
| 13× | unpow-prod-up |
| 11× | associate-+r- associate--r+ |
| 9× | sin-sum rem-exp-log |
| 6× | rem-cbrt-cube |
| 5× | pow-flip difference-cubes inv-pow associate-+l- |
| 4× | neg-sub0 un-div-inv |
| 3× | sqrt-unprod rem-square-sqrt |
| 2× | pow3 sum-cubes unpow2 distribute-rgt-out-- unsub-neg |
| 1× | associate--l- sqrt-undiv pow-neg distribute-frac-neg sub-div exp-to-pow cos-sum associate--r- distribute-rgt-out |
| 100× | intervals |
| 1.0m | 16169× | body | 10240 | exit |
| 50.6s | 459773× | body | 80 | valid |
| 32.3s | 31044× | body | 1280 | valid |
| 15.3s | 23726× | body | 640 | valid |
| 6.8s | 69248× | body | 80 | nan |
| 6.2s | 11802× | body | 320 | valid |
| 5.3s | 3116× | body | 1280 | nan |
| 3.0s | 2701× | body | 640 | nan |
| 2.7s | 10206× | body | 160 | valid |
| 1.7s | 49536× | pre | 80 | true |
| 1.4s | 1222× | body | 320 | nan |
| 1.3s | 1531× | body | 2560 | valid |
| 342.0ms | 597× | body | 5120 | valid |
| 311.0ms | 698× | body | 160 | nan |
529 calls:
| 25.5s | (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (/ (- (* 0.254829592 0.254829592) (* (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))))) (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))))))) (- 0.254829592 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0))))))))) (exp (- (* (fabs x) (fabs x)))))) |
| 3.5s | (/ (* (/ (/ (+ (* (+ (+ i alpha) beta) i) (* alpha beta)) (+ alpha (+ beta (* i 2.0)))) (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0)))) (/ (+ (+ i alpha) beta) (+ alpha (+ beta (* i 2.0))))) (/ (- (+ (+ (* 2.0 i) beta) alpha) (sqrt 1.0)) i)) |
| 3.0s | (* (/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (* (/ (+ (+ beta (* i 2.0)) (+ alpha (sqrt 1.0))) (+ (+ i alpha) beta)) (+ alpha (+ beta (* i 2.0))))) (/ (/ (sqrt (+ (* (+ (+ i alpha) beta) i) (* alpha beta))) (+ alpha (+ beta (* i 2.0)))) (/ (+ (+ beta (* i 2.0)) (- alpha (sqrt 1.0))) i))) |
| 1.8s | (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (* (/ 1.0 (- (* 1.0 1.0) (* (* (pow (fabs x) 2) 0.3275911) 0.3275911))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))) |
| 1.8s | (exp (log (- 1.0 (* (exp (- (pow (fabs x) 2))) (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 0.254829592 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ -0.284496736 (* (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (+ 1.421413741 (/ (* (+ -1.453152027 (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 0.3275911) (pow (fabs x) 2)))) (* (- 1.0 (* 0.3275911 (fabs x))) 1.061405429))) 1.0) (+ (* 0.3275911 (fabs x)) 1.0)))))))))))) |
Total 126.3b remaining (49.4%)
Threshold costs 4.8b (1.9%)
| 23.9b | 35% | math.sqrt on complex, real part |
| 17.5b | 44.1% | math.log10 on complex, real part |
| 17.0b | 46.7% | math.log/2 on complex, real part |
| 9.9b | 59.4% | math.log/1 on complex, real part |
| 9.6b | 59.5% | math.abs on complex |