| 78× | intervals |
| 4.4m | 33337× | body | 10240 | exit |
| 1.3m | 43487× | body | 1280 | valid |
| 27.6s | 30724× | body | 640 | valid |
| 18.2s | 203273× | body | 80 | valid |
| 13.2s | 151837× | body | 80 | nan |
| 10.8s | 27892× | body | 320 | valid |
| 8.3s | 36078× | body | 160 | valid |
| 7.7s | 170932× | pre | 80 | true |
| 2.2s | 3103× | body | 2560 | valid |
| 1.1s | 7662× | body | 160 | nan |
| 460.0ms | 4163× | pre | 10240 | exit |
| 167.0ms | 223× | body | 5120 | valid |
459 calls:
| 7.3s | (sqrt (+ (* (* (- lambda1 lambda2) (+ (log (* (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))))) (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2)))) |
| 4.1s | (cbrt (* (* (log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))) |
| 3.8s | (cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))) |
| 2.1s | (cbrt (* (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (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))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (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))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))) |
| 2.1s | (cbrt (* (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (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))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (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))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))))) |
| 144× | rewrite-expression-head |
459 calls:
| 20.0s | (- (* (* (* (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))) (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)))) (* (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))) (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))))) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))) (* (* (* x0 x0) (* (* (* x0 x0) (* x0 x0)) (* (* x0 x0) (* x0 x0)))) (* (* (* x0 x0) (* x0 x0)) (* (* x0 x0) (* x0 x0))))) |
| 2.4s | (- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0) |
| 1.8s | (* (* (* (* x0 x0) (* x0 x0)) (* x0 x0)) (* (* (* x0 x0) (* x0 x0)) (* x0 x0))) |
| 909.0ms | (/ (+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)) (* (cos lambda2) (* (cos lambda1) (cos phi2)))))) |
| 891.0ms | (cbrt (* (* (sin (/ (- lambda1 lambda2) 2.0)) (* (* (cbrt (sin (/ (- lambda1 lambda2) 2.0))) (cbrt (sin (/ (- lambda1 lambda2) 2.0)))) (cbrt (sin (/ (- lambda1 lambda2) 2.0))))) (sin (/ (- lambda1 lambda2) 2.0)))) |
| 129798× | pow1 |
| 75335× | pow-prod-up |
| 26325× | pow-plus |
| 25489× | pow-prod-down |
| 24705× | pow-sqr |
| 14198× | pow2 |
| 13940× | times-frac |
| 10316× | *-un-lft-identity |
| 9361× | sqrt-prod |
| 8129× | add-sqr-sqrt |
| 6925× | add-cube-cbrt |
| 3755× | add-exp-log |
| 3087× | add-cbrt-cube |
| 1833× | prod-exp |
| 1495× | cbrt-unprod |
| 1346× | distribute-lft-out |
| 1007× | associate-/l* |
| 851× | sqrt-div |
| 815× | frac-times |
| 769× | div-exp |
| 763× | associate-*l/ |
| 756× | associate-*r* |
| 743× | flip-- |
| 742× | flip3-- |
| 709× | add-log-exp |
| 688× | frac-add |
| 591× | associate-*l* |
| 571× | associate-*r/ |
| 514× | div-inv |
| 481× | associate-/r* |
| 473× | cbrt-undiv |
| 459× | flip-+ |
| 458× | flip3-+ |
| 411× | associate-/r/ |
| 377× | difference-of-squares |
| 307× | distribute-lft-out-- |
| 298× | cbrt-div |
| 269× | pow-exp |
| 268× | cbrt-prod |
| 239× | sin-mult |
| 212× | cos-mult |
| 206× | swap-sqr |
| 188× | pow-to-exp |
| 163× | unswap-sqr |
| 160× | log-prod |
| 123× | frac-2neg clear-num exp-prod |
| 114× | pow3 |
| 109× | sub-neg |
| 108× | *-commutative |
| 94× | associate-/l/ |
| 89× | diff-log |
| 57× | unpow-prod-down log-pow |
| 55× | pow1/3 |
| 53× | distribute-rgt-neg-in |
| 49× | frac-sub |
| 47× | sum-log |
| 46× | log-div |
| 44× | distribute-rgt-in distribute-lft-in |
| 43× | sqrt-pow1 pow1/2 |
| 34× | div-sub |
| 32× | distribute-lft-neg-in |
| 30× | rem-sqrt-square |
| 28× | +-commutative |
| 25× | distribute-rgt-out |
| 22× | rem-log-exp |
| 20× | 1-exp rec-exp |
| 19× | associate--l+ |
| 18× | tan-quot |
| 16× | cos-diff |
| 15× | cos-sum |
| 14× | sin-diff |
| 13× | cube-unmult associate--r+ |
| 12× | neg-mul-1 distribute-rgt1-in |
| 11× | neg-sub0 sqr-pow |
| 10× | exp-diff associate-+r+ |
| 9× | associate--l- pow-unpow acos-asin |
| 7× | sin-cos-mult exp-neg |
| 6× | associate-+l+ exp-sum associate--r- |
| 5× | distribute-lft-neg-out sin-sum pow-flip neg-log sum-cubes inv-pow |
| 4× | associate-+r- pow-pow un-div-inv rem-cbrt-cube |
| 3× | distribute-rgt-neg-out distribute-frac-neg distribute-neg-frac asin-acos rem-exp-log acos-neg |
| 2× | distribute-lft1-in rem-cube-cbrt pow-div associate-+l- sqr-cos |
| 1× | quot-tan cube-prod unsub-neg unpow3 sqrt-unprod tanh-undef cube-mult tanh-def difference-cubes rem-square-sqrt cube-div |
Total 63.2b remaining (30%)
Threshold costs 6.3b (3%)
| 7.5b | 45.2% | Quadratic roots, narrow range |
| 7.4b | 45.8% | Cubic critical, narrow range |
| 6.9b | 0% | Quadratic roots, medium range |
| 6.3b | 61.9% | Equirectangular approximation to distance on a great circle |
| 6.3b | 44.2% | Quotient of products |