Details

prune11.5m (43.8%)

sample7.3m (27.8%)

Algorithm
77×intervals
Results
4.0m30960×body10240exit
1.3m42265×body1280valid
26.5s29093×body640valid
17.8s198711×body80valid
14.4s152461×body80nan
13.0s26586×body320valid
9.6s168178×pre80true
8.3s36177×body160valid
2.3s3111×body2560valid
968.0ms8100×body160nan
471.0ms4031×pre10240exit
237.0ms202×body5120valid
157.0ms8350×pre80false
1.0msbody640nan

simplify5.2m (19.8%)

series58.5s (3.7%)

Calls

482 calls:

1.2s
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
1.2s
(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
793.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* (log 0.5) c_p) (+ (* 0.5 (* t c_p)) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
748.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))
686.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite57.6s (3.6%)

Algorithm
143×rewrite-expression-head
Calls

482 calls:

6.8s
(/ (- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x))))))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (cbrt (- 1.0 x))))
3.2s
(- (* (* x (* (* (cbrt (+ (* 1.0 1.0) (* x (- x 1.0)))) (cbrt (- 1.0 x))) (- (pow x 3) (pow 1.0 3)))) (cbrt (- 1.0 x))) (* (+ (* x x) (+ (* 1.0 1.0) (* x 1.0))) (* (+ x 1.0) (* (* (cbrt (- (* 1.0 1.0) (* x x))) (cbrt (+ (pow 1.0 3) (pow x 3)))) (cbrt (- (* 1.0 1.0) (* x x)))))))
1.1s
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))
925.0ms
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
723.0ms
(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))))
Rules
183138×frac-times
178920×cbrt-div
97368×associate-*r/
86905×associate-*l/
83787×flip--
83786×flip3--
54969×flip-+
54968×flip3-+
40834×frac-sub
19463×associate-/l/
7811×times-frac
6612×add-sqr-sqrt
6579×*-un-lft-identity
6130×sqrt-div
5995×frac-add
4337×add-cube-cbrt
3242×add-exp-log
1920×add-cbrt-cube
1641×sqrt-prod
1085×prod-exp
1055×div-exp
1051×pow1
1013×associate-*r*
813×associate-/l*
809×difference-of-squares
751×add-log-exp
682×cbrt-prod
654×associate-/r*
619×unpow-prod-down
597×associate-*l*
569×distribute-lft-out--
506×distribute-lft-out
476×cbrt-undiv
469×cbrt-unprod
445×cube-prod
412×div-inv
369×pow-exp
332×associate-/r/
275×unswap-sqr
272×log-prod
269×pow-to-exp
250×swap-sqr
245×sqr-pow
217×pow-prod-down
186×distribute-rgt-neg-in
127×clear-num frac-2neg
109×*-commutative
96×sub-neg
92×1-exp rec-exp
86×diff-log
75×log-pow
68×pow1/2 sqrt-pow1
67×unpow3 cube-mult
56×exp-prod sum-log
51×pow-unpow
47×div-sub
45×distribute-rgt-in pow-flip distribute-lft-in
44×pow1/3
35×pow-prod-up unpow2
34×rem-sqrt-square
33×+-commutative
29×pow-sqr
27×log-div
24×neg-sub0 tan-quot
22×pow-pow
20×associate--l-
19×inv-pow associate--l+
18×pow-plus distribute-rgt-out neg-log rem-log-exp sin-diff
17×cos-diff
16×pow2 sin-mult
15×rem-cube-cbrt difference-cubes
14×acos-asin associate-+l-
13×sin-cos-mult associate-+r-
12×cube-div cos-sum
10×un-div-inv
associate-+r+
sqrt-unprod
cos-mult
acos-neg distribute-frac-neg
sqrt-undiv sin-sum asin-acos
distribute-lft-neg-out distribute-rgt-neg-out tanh-def
distribute-lft-neg-in exp-to-pow
exp-diff sum-cubes rem-exp-log distribute-lft1-in unsub-neg rem-square-sqrt sub-div sqr-cos rem-cbrt-cube
sin-neg distribute-rgt-out-- sqr-sin associate-+l+ tanh-undef neg-mul-1 associate--r- associate--r+

regimes13.8s (0.9%)

Accuracy

Total 41.0b remaining (27.3%)

Threshold costs 6.7b (4.5%)

7.6b45.4%Quadratic roots, narrow range
7.5b45.5%Cubic critical, narrow range
4.9b56.7%Quotient of products
4.7b68.4%Equirectangular approximation to distance on a great circle
3.1b88.7%Quadratic roots, full range

localize4.4s (0.3%)

bsearch953.0ms (0.1%)

end2.0ms (0.0%)