| 78× | intervals |
| 8.7m | 53096× | body | 10240 | exit |
| 1.3m | 43533× | body | 1280 | valid |
| 29.8s | 30666× | body | 640 | valid |
| 19.9s | 205226× | body | 80 | valid |
| 13.5s | 152994× | body | 80 | nan |
| 12.6s | 27463× | body | 320 | valid |
| 9.9s | 193340× | pre | 80 | true |
| 8.1s | 36345× | body | 160 | valid |
| 1.7s | 2995× | body | 2560 | valid |
| 891.0ms | 7986× | body | 160 | nan |
| 474.0ms | 4034× | pre | 10240 | exit |
| 241.0ms | 214× | body | 5120 | valid |
| 204.0ms | 8545× | pre | 80 | false |
| 2.0ms | 1× | body | 640 | nan |
500 calls:
| 8.2s | (/ (/ (* (* 3.0 a) c) (cbrt (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a) |
| 2.7s | (/ (- (pow (cos delta) 3) (pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)) (+ (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta))))) |
| 1.8s | (+ (pow (cos phi1) 3) (pow (* (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda2) (cos lambda1))) (cos phi2)) 3)) |
| 1.6s | (/ (+ (* (cos delta) (cos delta)) (+ (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))) (* (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))) (/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))) |
| 1.3s | (/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))) |
| 150× | rewrite-expression-head |
500 calls:
| 2.7s | (* (- (/ (sqrt m) (/ (/ v (- 1.0 m)) (sqrt m))) 1.0) m) |
| 1.0s | (* (/ (pow x 2) (log 2.0)) (- (+ (/ 0.125 (log 2.0)) (/ 1/2 (pow 2.0 2))) 0.25)) |
| 971.0ms | (/ (* (* (cos phi2) (- (* (* (cos lambda1) (cos lambda2)) (* (cos lambda1) (cos lambda2))) (* (* (sin lambda2) (sin lambda2)) (* (sin lambda1) (sin lambda1))))) (cos phi1)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) |
| 801.0ms | (* (/ 2.0 (+ (pow (exp x) 3) (exp (* x -3)))) (+ (* (exp x) (exp x)) (- (* (exp (- x)) (exp (- x))) (* (exp x) (exp (- x)))))) |
| 647.0ms | (sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (* (cos (/ (+ phi1 phi2) 2.0)) (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2)))) |
| 9689× | times-frac |
| 7748× | add-sqr-sqrt |
| 7612× | *-un-lft-identity |
| 5251× | add-cube-cbrt |
| 3022× | add-exp-log |
| 2864× | sqrt-prod |
| 1914× | add-cbrt-cube |
| 1213× | pow1 |
| 1083× | flip-- |
| 1082× | flip3-- |
| 1001× | prod-exp |
| 959× | sqrt-div |
| 939× | difference-of-squares |
| 935× | div-exp |
| 906× | associate-*r* |
| 875× | associate-/r* |
| 871× | frac-times |
| 849× | associate-*l/ |
| 769× | distribute-lft-out-- |
| 749× | associate-/l* add-log-exp |
| 734× | cbrt-prod |
| 598× | associate-*l* |
| 545× | unpow-prod-down |
| 492× | associate-*r/ |
| 464× | cbrt-undiv |
| 462× | cbrt-unprod |
| 445× | div-inv |
| 428× | frac-add |
| 401× | distribute-lft-out |
| 374× | associate-/r/ |
| 369× | pow-exp |
| 299× | cube-prod |
| 292× | pow-prod-down |
| 269× | pow-to-exp |
| 251× | cbrt-div |
| 237× | flip-+ sqr-pow |
| 236× | flip3-+ |
| 230× | unswap-sqr |
| 181× | log-prod |
| 175× | log-pow |
| 166× | swap-sqr |
| 156× | distribute-rgt-neg-in |
| 139× | sqrt-pow1 |
| 135× | associate-/l/ |
| 131× | clear-num frac-2neg |
| 128× | exp-prod |
| 127× | cos-mult |
| 117× | *-commutative |
| 107× | sub-neg |
| 95× | pow1/2 |
| 83× | diff-log |
| 62× | frac-sub |
| 61× | exp-neg |
| 60× | sin-mult |
| 56× | sum-log |
| 55× | neg-sub0 |
| 54× | pow-prod-up |
| 53× | pow1/3 |
| 47× | log-div |
| 46× | div-sub |
| 43× | exp-diff |
| 42× | +-commutative |
| 39× | distribute-rgt-in distribute-lft-in 1-exp |
| 38× | pow-sqr rec-exp |
| 36× | pow-unpow rem-sqrt-square |
| 35× | unpow3 cube-mult |
| 30× | tan-quot |
| 29× | associate-+r+ |
| 26× | sub-div |
| 25× | exp-sum |
| 24× | cube-div un-div-inv |
| 23× | pow-plus rem-log-exp |
| 20× | sin-cos-mult |
| 19× | unpow2 pow2 pow-pow |
| 18× | associate-+l+ |
| 17× | cos-diff |
| 16× | distribute-rgt-out |
| 14× | rem-cube-cbrt |
| 13× | associate-+r- associate--l+ |
| 12× | associate-+l- cos-sum sin-diff |
| 11× | sqrt-unprod distribute-neg-in neg-log |
| 10× | acos-asin |
| 9× | distribute-lft-neg-in associate--r+ |
| 8× | pow-flip rem-cbrt-cube |
| 6× | acos-neg rem-exp-log associate--l- inv-pow distribute-frac-neg associate--r- |
| 5× | difference-cubes sin-sum distribute-rgt-out-- sqrt-undiv |
| 3× | rem-square-sqrt neg-mul-1 |
| 2× | sin-neg distribute-lft1-in pow3 asin-acos sqr-cos distribute-rgt-neg-out |
| 1× | rgt-mult-inverse sum-cubes sqr-sin tanh-undef tanh-def |
Total 39.0b remaining (25%)
Threshold costs 6.5b (4.1%)
| 7.2b | 47.3% | Quadratic roots, narrow range |
| 6.7b | 3.6% | Quadratic roots, medium range |
| 6.2b | 10.9% | Cubic critical, medium range |
| 4.1b | 70.6% | Equirectangular approximation to distance on a great circle |
| 3.3b | 87.8% | Cubic critical |