Details

sample4.7m (37.9%)

Algorithm
77×intervals
Results
1.7m42973×body1280valid
40.2s31301×body640valid
28.0s201437×body80valid
25.7s14854×body10240exit
19.4s27952×body320valid
19.4s152623×body80nan
13.8s36233×body160valid
9.8s150526×pre80true
2.8s2949×body2560valid
1.7s8027×body160nan
1.2s4101×pre10240exit
221.0ms192×body5120valid
3.0ms1×body640nan
2.0ms1×body320nan

prune3.3m (26.7%)

simplify2.9m (23.8%)

series41.9s (5.7%)

Calls

444 calls:

1.2s
(/ (- (* (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))))))))
783.0ms
(- (* (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))))))))
775.0ms
(- (* (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)))))))))
665.0ms
(- (* (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))))))))
608.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))

regimes20.1s (2.7%)

Accuracy

Total 61.5b remaining (29.7%)

Threshold costs 5.1b (2.5%)

7.6b45.1%Quadratic roots, narrow range
7.5b44.3%Cubic critical, narrow range
6.2b6.9%Quadratic roots, medium range
6.2b6.1%Cubic critical, medium range
6.2b56.8%Equirectangular approximation to distance on a great circle

rewrite16.4s (2.2%)

Algorithm
139×rewrite-expression-head
Calls

444 calls:

664.0ms
(/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a)))
457.0ms
(cbrt (/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a))))
428.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (- lambda1 lambda2) (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- phi1 phi2) (- phi1 phi2))))
400.0ms
(/ (+ (exp (* x 3)) (/ -1 (exp (* x 3)))) (+ (+ 1 (* (exp x) (exp x))) (exp (* x -2))))
398.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (* (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))))) (cbrt (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))))) (* (- phi1 phi2) (- phi1 phi2))))
Rules
3881×add-exp-log
3877×add-sqr-sqrt
3746×*-un-lft-identity
3700×add-cbrt-cube
3511×times-frac
3078×associate-*l/
2530×add-cube-cbrt
2156×frac-times
1989×flip--
1988×flip3--
1560×cbrt-div
1449×prod-exp
1391×cbrt-unprod
1260×div-exp
1201×cbrt-undiv
1186×pow1
1067×associate-*r/
1030×frac-add
984×sqrt-div
778×associate-*r*
774×sqrt-prod
677×add-log-exp
637×associate-*l*
444×insert-posit16
413×associate-/r*
392×difference-of-squares
355×associate-/l*
339×distribute-lft-out
264×cbrt-prod
260×pow-prod-down
255×div-inv
244×flip-+
243×flip3-+
216×unswap-sqr
208×distribute-lft-out--
164×log-prod
142×associate-/r/
119×*-commutative
103×swap-sqr
102×cos-mult
101×frac-2neg clear-num exp-prod
99×tanh-def
89×pow-prod-up
82×sub-neg
76×log-pow
70×associate-/l/
68×pow-plus
64×diff-log
62×sum-log
52×associate-+r+
51×pow-sqr
49×difference-of-sqr-1
48×sqrt-pow1
46×sin-mult
44×distribute-rgt-in distribute-lft-in
39×pow1/3
38×pow2
37×+-commutative div-sub
36×1-exp log-div
34×pow1/2
32×associate-+l+ tan-quot
31×rem-sqrt-square
28×cos-diff
23×rec-exp
22×pow-flip
20×unpow-prod-down
19×frac-sub
18×rem-log-exp
14×distribute-rgt-out
13×cos-sum
12×inv-pow
11×pow3
10×associate--l+ sqr-pow acos-asin
9×sin-cos-mult
8×sub-div
6×sin-sum distribute-rgt-neg-in sqr-cos distribute-lft-neg-in
5×pow-exp pow-to-exp distribute-rgt-out-- associate-+l- sin-diff
4×exp-diff associate--l- associate-+r- cube-unmult rem-cbrt-cube
3×distribute-lft-neg-out exp-sum distribute-frac-neg un-div-inv asin-acos rem-exp-log acos-neg
2×distribute-rgt1-in
1×sqrt-undiv unsub-neg neg-mul-1 associate--r+ difference-cubes tanh-undef exp-to-pow

localize6.2s (0.8%)

bsearch953.0ms (0.1%)

end1.0ms (0.0%)