| 78× | intervals |
| 8.1m | 51433× | body | 10240 | exit |
| 58.3s | 44179× | body | 1280 | valid |
| 20.1s | 30315× | body | 640 | valid |
| 14.5s | 204702× | body | 80 | valid |
| 10.7s | 152738× | body | 80 | nan |
| 9.4s | 27515× | body | 320 | valid |
| 7.3s | 189961× | pre | 80 | true |
| 6.0s | 36369× | body | 160 | valid |
| 1.9s | 2910× | body | 2560 | valid |
| 566.0ms | 7816× | body | 160 | nan |
| 454.0ms | 8075× | pre | 80 | false |
| 428.0ms | 4048× | pre | 10240 | exit |
| 249.0ms | 273× | body | 5120 | valid |
| 2.0ms | 3× | body | 640 | nan |
515 calls:
| 4.9s | (/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1)))) |
| 1.6s | (- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0)))) |
| 769.0ms | (exp (log (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2)))))) |
| 663.0ms | (/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))) |
| 637.0ms | (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))) |
| 146× | rewrite-expression-head |
515 calls:
| 5.0s | (- (/ (/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) 1.0) |
| 751.0ms | (- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3))) |
| 704.0ms | (/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0))))) |
| 703.0ms | (* (* (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))) |
| 519.0ms | (sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2)))) |
| 8143× | times-frac |
| 7806× | *-un-lft-identity |
| 7158× | add-sqr-sqrt |
| 4432× | add-cube-cbrt |
| 2686× | add-exp-log |
| 1724× | add-cbrt-cube |
| 1594× | sqrt-prod |
| 1206× | associate-*r* |
| 1132× | distribute-lft-out-- |
| 1085× | pow1 |
| 1037× | associate-*l/ |
| 1023× | flip-- |
| 1007× | unpow-prod-down |
| 1001× | flip3-- |
| 952× | difference-of-squares |
| 876× | associate-/l* |
| 825× | prod-exp |
| 823× | div-exp |
| 812× | add-log-exp |
| 682× | frac-times |
| 677× | cbrt-prod |
| 674× | distribute-lft-out |
| 669× | cube-prod |
| 660× | associate-/r* |
| 650× | frac-add |
| 618× | sqrt-div |
| 472× | associate-*l* |
| 470× | associate-*r/ |
| 413× | cbrt-div |
| 409× | div-inv |
| 398× | cbrt-undiv |
| 383× | cbrt-unprod |
| 356× | distribute-rgt-neg-in |
| 343× | associate-/r/ |
| 326× | pow-exp |
| 316× | flip-+ |
| 294× | flip3-+ |
| 255× | sqr-pow |
| 241× | pow-to-exp |
| 228× | pow-prod-down |
| 214× | unswap-sqr |
| 153× | log-prod |
| 127× | swap-sqr |
| 124× | clear-num frac-2neg |
| 120× | sub-neg |
| 119× | associate-/l/ |
| 108× | distribute-lft-neg-in pow1/3 |
| 106× | *-commutative |
| 95× | diff-log log-div |
| 71× | exp-diff |
| 67× | unpow3 cube-mult |
| 65× | 1-exp |
| 62× | sum-log |
| 61× | div-sub |
| 60× | pow-unpow log-pow |
| 59× | exp-prod |
| 53× | unpow2 |
| 45× | +-commutative rec-exp |
| 43× | pow-prod-up |
| 42× | neg-sub0 |
| 41× | distribute-rgt-in distribute-lft-in sqrt-pow1 |
| 39× | pow1/2 rem-sqrt-square |
| 36× | exp-sum |
| 35× | neg-mul-1 |
| 34× | cube-div |
| 31× | pow-sqr associate-+l- associate--l+ |
| 29× | sin-mult |
| 28× | distribute-rgt-out |
| 27× | pow-plus cos-mult |
| 26× | frac-sub |
| 25× | associate-+r+ |
| 24× | pow-pow |
| 23× | neg-log |
| 18× | associate--l- rem-log-exp |
| 17× | pow2 |
| 15× | cos-diff sin-diff |
| 14× | pow-flip |
| 13× | cos-sum rem-cube-cbrt |
| 12× | tan-quot distribute-rgt-neg-out |
| 11× | sin-sum rem-cbrt-cube |
| 10× | associate-+l+ |
| 8× | sin-cos-mult rem-exp-log inv-pow acos-asin associate-+r- |
| 7× | distribute-frac-neg |
| 6× | sub-div |
| 5× | difference-cubes distribute-lft1-in pow3 |
| 4× | sin-neg sum-cubes unsub-neg |
| 3× | acos-neg associate--r- associate--r+ |
| 2× | un-div-inv pow-sub distribute-neg-frac pow-neg tanh-def |
| 1× | distribute-neg-out unpow1/3 sqrt-unprod sqr-sin tanh-undef asin-acos |
Total 26.4b remaining (20.5%)
Threshold costs 6.4b (5%)
| 4.9b | 54.7% | Quotient of products |
| 4.8b | 83.1% | Cubic critical |
| 3.5b | 74.5% | Equirectangular approximation to distance on a great circle |
| 3.3b | 87.9% | Quadratic roots, full range |
| 1.3b | 0% | 2-ancestry mixing, positive discriminant |