Details

sample28.8m (73.7%)

Algorithm
72×intervals
Results
7.6m80199×body10240exit
53.7s33308×body1280valid
25.1s197506×body80valid
22.0s24182×body640valid
20.0s151768×body80nan
13.7s25099×body320valid
12.4s35307×body160valid
9.3s153484×pre80true
3.3s3105×body2560valid
1.9s7981×body160nan
1.0s4125×pre10240exit
277.0ms238×body5120valid

prune5.0m (12.7%)

simplify4.0m (10.3%)

series36.6s (1.6%)

Calls

394 calls:

Slowest
719.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (+ 1 (* c_p (+ (* 1/2 t) (log 1/2)))) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
601.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (cbrt (* (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))) (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
577.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
572.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
551.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (- lambda1 lambda2)) (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite21.1s (0.9%)

Algorithm
125×rewrite-expression-head
Calls

394 calls:

Slowest
6.1s
(* (/ (/ (cbrt a2) (cbrt (/ b2 (cbrt a2)))) (cbrt (/ b2 (cbrt a2)))) (/ (/ a1 (/ b1 (cbrt a2))) (cbrt (/ b2 (cbrt a2)))))
516.0ms
(/ (- (* (* (/ x (+ 1 x)) (* x (/ x (+ 1 x)))) (- x 1)) (* (+ 1 x) (* (+ 1 x) (* (/ (+ 1 x) (- x 1)) (/ (+ 1 x) (- x 1)))))) (* (+ (* (/ (+ 1 x) (- x 1)) (/ (+ 1 x) (- x 1))) (* (/ x (+ 1 x)) (+ (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))) (* (+ 1 x) (- x 1))))
427.0ms
(* (* (+ (/ 1 (- x 1)) (/ x (+ x 1))) (+ (/ 1 (- x 1)) (/ x (+ x 1)))) (+ (/ 1 (- x 1)) (/ x (+ x 1))))
413.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
396.0ms
(/ (- (* (/ x (+ 1 x)) (* (/ x (+ 1 x)) (/ x (+ 1 x)))) (* (/ (+ 1 x) (- x 1)) (* (/ (+ 1 x) (- x 1)) (/ (+ 1 x) (- x 1))))) (+ (* (/ (+ 1 x) (- x 1)) (/ (+ 1 x) (- x 1))) (* (/ x (+ 1 x)) (+ (/ x (+ 1 x)) (/ (+ 1 x) (- x 1))))))
Rules
31103×times-frac
18047×add-sqr-sqrt
17021×cbrt-prod
13676×*-un-lft-identity
12616×add-cube-cbrt
7952×add-exp-log
6262×add-cbrt-cube
4292×associate-*l*
3764×frac-times
3757×prod-exp
2885×div-exp
2870×cbrt-unprod
2497×associate-*r/
2329×associate-*r*
2248×associate-*l/
2089×cbrt-undiv
1611×pow1
1375×flip--
1374×flip3--
1161×frac-add
1074×div-inv
969×flip-+
968×flip3-+
901×frac-sub
792×pow-exp
745×unswap-sqr
638×associate-/r*
626×sqrt-div
599×add-log-exp
520×associate-/l/
471×associate-/r/
410×associate-/l*
405×pow-prod-down pow-to-exp
394×insert-posit16
365×cos-mult
342×difference-of-squares
317×sqrt-prod
301×distribute-lft-out
278×cbrt-div
216×pow-prod-up
213×distribute-rgt-neg-in
204×distribute-lft-neg-in
178×distribute-lft-out--
167×1-exp rec-exp
132×pow-sqr
128×log-prod
121×pow-plus
109×swap-sqr
104×frac-2neg clear-num
103×*-commutative
100×tan-quot
92×sub-neg
81×pow2
74×unpow-prod-down
72×diff-log
68×neg-mul-1
42×sqrt-pow1 pow1/2
41×difference-of-sqr--1
40×rem-sqrt-square
37×sum-log
36×log-div
34×distribute-rgt-in distribute-lft-in
31×pow1/3
27×div-sub log-pow
25×+-commutative
17×distribute-rgt-out
15×exp-prod
14×difference-of-sqr-1 acos-asin rem-log-exp
13×associate-+r+ cube-unmult sqr-pow
12×cos-diff
11×cos-sum
10×associate--l+ associate-+l-
pow-unpow pow-pow
associate--r+
pow-flip associate-+l+ associate--l- inv-pow associate--r-
sin-mult distribute-rgt1-in
difference-cubes
neg-sub0 distribute-frac-neg exp-sum pow3 neg-log distribute-lft-neg-out un-div-inv
exp-diff associate-+r- rem-exp-log acos-neg
remove-posit16 sin-sum distribute-rgt-out-- distribute-neg-frac asin-acos
unsub-neg sin-cos-mult distribute-rgt-neg-out tanh-undef tanh-def sqr-cos sin-diff

regimes12.2s (0.5%)

Accuracy

Total 61.1b remaining (33.1%)

Threshold costs 4.0b (2.2%)

8.6b35.9%Equirectangular approximation to distance on a great circle
7.6b42.8%Cubic critical, narrow range
7.3b45.7%Quadratic roots, narrow range
6.4b4.2%Cubic critical, medium range
6.2b11.3%Quadratic roots, medium range

localize4.4s (0.2%)

bsearch1.7s (0.1%)

end1.0ms (0.0%)