| 78× | intervals |
| 5.0m | 26288× | body | 10240 | exit |
| 1.9m | 43571× | body | 1280 | valid |
| 38.9s | 30540× | body | 640 | valid |
| 27.2s | 202536× | body | 80 | valid |
| 18.5s | 150771× | body | 80 | nan |
| 18.1s | 27686× | body | 320 | valid |
| 12.7s | 36538× | body | 160 | valid |
| 10.7s | 163277× | pre | 80 | true |
| 2.6s | 3037× | body | 2560 | valid |
| 1.5s | 4104× | pre | 10240 | exit |
| 1.0s | 8004× | body | 160 | nan |
| 295.0ms | 202× | body | 5120 | valid |
| 1.0ms | 1× | body | 320 | nan |
468 calls:
| 8.4s | (/ (+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))))) |
| 2.7s | (+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))) |
| 1.7s | (- (pow (cos delta) 3) (* (pow (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) 3) (* (sin phi1) (* (sin phi1) (sin phi1))))) |
| 1.7s | (- (pow (cos delta) 3) (* (* (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1)))))) (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1)))))) (* (* (sin phi1) (sin phi1)) (sin phi1)))) |
| 1.7s | (- (pow (cos delta) 3) (pow (* (sin (asin (+ (* (cos theta) (* (sin delta) (cos phi1))) (* (cos delta) (sin phi1))))) (sin phi1)) 3)) |
| 145× | rewrite-expression-head |
468 calls:
| 2.3s | (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)))) |
| 1.8s | (/ (+ (* (* (cos phi1) (cos phi1)) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2))))))) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (- (* (cos phi2) (+ (* (cos lambda2) (cos lambda1)) (* (sin lambda1) (sin lambda2)))) (cos phi1))))) |
| 1.2s | (sqrt (* (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2)))) (cbrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2)))))) |
| 1.2s | (- (* (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0)))) (* (* (cbrt (/ x (+ x 1.0))) (cbrt (/ x (+ x 1.0)))) (cbrt (/ x (+ x 1.0))))) (* (/ (+ x 1.0) (- x 1.0)) (/ (+ x 1.0) (- x 1.0)))) |
| 886.0ms | (* (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))) (sqrt (- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n))))) |
| 14787× | frac-times |
| 13698× | flip-- |
| 13697× | flip3-- |
| 12580× | associate-*r/ |
| 12298× | associate-*l/ |
| 9999× | cbrt-div |
| 9562× | frac-add |
| 4802× | sqrt-div |
| 3905× | *-un-lft-identity |
| 3819× | times-frac |
| 3607× | add-sqr-sqrt |
| 2905× | add-exp-log |
| 2678× | add-cube-cbrt |
| 2089× | add-cbrt-cube |
| 1356× | pow1 |
| 1194× | sqrt-prod |
| 1037× | prod-exp |
| 820× | div-exp |
| 726× | add-log-exp |
| 722× | flip-+ |
| 721× | flip3-+ |
| 636× | cbrt-unprod |
| 547× | associate-*r* |
| 542× | associate-*l* |
| 483× | associate-/r* |
| 461× | cbrt-undiv |
| 362× | associate-/l* |
| 354× | distribute-lft-out |
| 342× | pow-prod-down |
| 335× | cos-mult |
| 307× | cbrt-prod |
| 301× | difference-of-squares |
| 279× | pow-exp |
| 263× | div-inv |
| 262× | tan-quot |
| 251× | frac-sub |
| 243× | distribute-lft-out-- |
| 222× | associate-/r/ |
| 201× | sin-mult |
| 197× | pow-to-exp |
| 187× | associate-/l/ |
| 144× | unswap-sqr |
| 132× | log-prod |
| 123× | *-commutative |
| 115× | unpow-prod-down |
| 105× | pow-prod-up clear-num frac-2neg |
| 103× | sub-neg |
| 77× | swap-sqr |
| 73× | diff-log |
| 66× | distribute-rgt-in distribute-lft-in sum-log |
| 65× | pow-sqr |
| 64× | exp-prod |
| 59× | sqrt-pow1 |
| 55× | pow-plus |
| 52× | log-pow |
| 51× | pow1/2 |
| 49× | pow1/3 |
| 42× | sin-cos-mult log-div |
| 41× | sqr-pow |
| 40× | +-commutative |
| 38× | pow2 |
| 37× | 1-exp rec-exp |
| 35× | div-sub |
| 31× | rem-sqrt-square associate-+r+ |
| 30× | distribute-rgt-neg-in |
| 27× | associate--l+ |
| 21× | cos-diff sub-div |
| 19× | rem-log-exp |
| 18× | distribute-lft-neg-in |
| 17× | sin-diff |
| 16× | pow3 |
| 15× | pow-unpow |
| 14× | neg-sub0 |
| 13× | associate--r+ |
| 12× | distribute-rgt-out cos-sum |
| 11× | pow-pow |
| 10× | cube-unmult associate--l- |
| 9× | sin-sum |
| 8× | distribute-frac-neg distribute-rgt-neg-out associate-+l- |
| 7× | associate-+r- cube-prod acos-asin asin-acos |
| 6× | difference-cubes associate--r- exp-sum |
| 5× | rem-cube-cbrt sin-neg sum-cubes rem-exp-log sqrt-undiv neg-mul-1 |
| 4× | cube-div pow-flip neg-log |
| 3× | acos-neg unpow3 sqrt-unprod inv-pow cube-mult rem-cbrt-cube |
| 2× | un-div-inv distribute-lft1-in distribute-lft-neg-out rem-square-sqrt tanh-def |
| 1× | exp-diff sqr-sin tanh-undef exp-to-pow |
Total 62.3b remaining (32.1%)
Threshold costs 4.6b (2.4%)
| 9.5b | 33.8% | Equirectangular approximation to distance on a great circle |
| 8.4b | 38.2% | Quadratic roots, narrow range |
| 5.9b | 15.1% | Quadratic roots, medium range |
| 5.5b | 59% | Cubic critical, narrow range |
| 5.2b | 82.1% | Quadratic roots, full range |