Details

sample10.3m

Algorithm
72×intervals
Results
7.3m81004×body10240exit
51.1s32894×body1280valid
25.3s198293×body80valid
21.3s24765×body640valid
21.3s151777×body80nan
13.1s25141×body320valid
12.2s34918×body160valid
11.2s154147×pre80true
2.8s2982×body2560valid
1.4s7801×body160nan
1.2s4132×pre10240exit
208.0ms235×body5120valid

prune3.3m

simplify1.5m

bsearch46.2s

series36.6s

Calls

407 calls:

Slowest
649.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
632.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
606.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
575.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
537.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite14.3s

Algorithm
129×rewrite-expression-head
Calls

407 calls:

Slowest
609.0ms
(- (+ (* (log (/ 1 (+ 1 (exp (- s))))) c_p) (* (log (- 1 (/ 1 (+ 1 (exp (- s)))))) c_n)) (+ (* (- (+ (* 1/2 t) (log 1/2)) (* 1/8 (* t t))) c_p) (- (* c_n (log 1/2)) (+ (* (* (* 1/8 t) t) c_n) (* (* 1/2 t) c_n)))))
550.0ms
(* (/ (exp a) (+ (* (* (exp a) (exp a)) (exp a)) (* (* (exp b) (exp b)) (exp b)))) (+ (* (exp b) (exp b)) (- (* (exp a) (exp a)) (* (exp b) (exp a)))))
496.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
357.0ms
(log (+ x (+ x (+ (/ -1/8 (* (* x x) x)) (/ 1/2 x)))))
327.0ms
(sin (- lambda1 lambda2))
Rules
13056×times-frac
8242×*-un-lft-identity
8182×add-sqr-sqrt
5416×add-cube-cbrt
3620×add-exp-log
3227×difference-of-squares
2325×add-cbrt-cube
2100×cbrt-prod
1396×difference-of-sqr-1
1375×prod-exp
1374×div-exp
1294×associate-*l/
1219×sqrt-prod flip--
1218×flip3--
1196×pow1
732×cbrt-undiv
731×frac-times
726×associate-*r*
712×sqrt-div
698×pow-exp
687×add-log-exp
679×cbrt-unprod
597×associate-/l* frac-add
517×associate-/r/
499×associate-/r*
486×associate-*l*
476×div-inv
437×associate-*r/
407×insert-posit16
369×distribute-lft-out
350×pow-to-exp
270×distribute-lft-out--
264×pow-prod-down
222×log-prod
169×unswap-sqr
163×flip-+
162×flip3-+ swap-sqr
143×rec-exp
141×1-exp
125×log-pow
111×frac-2neg clear-num
102×diff-log
100×pow-prod-up
99×exp-prod
95×sub-neg
94×*-commutative
91×frac-sub
72×tan-quot
68×unpow-prod-down
66×associate-/l/
64×pow-plus
63×pow-sqr
58×sum-log
55×sqrt-pow1
53×pow1/2
40×cbrt-div pow2
37×rem-sqrt-square
36×rem-log-exp log-div
33×pow1/3
30×div-sub
29×pow-flip
27×distribute-rgt-out--
24×+-commutative
23×inv-pow
20×distribute-rgt-in distribute-lft-in
19×pow3
17×associate--l+
16×sqr-pow
13×acos-asin
12×pow-div
11×cos-diff
10×difference-of-sqr--1 associate--l- cos-sum
exp-sum neg-mul-1 distribute-rgt-neg-in distribute-lft-neg-in
sum-cubes
pow-unpow sin-mult associate--r+ pow-pow associate-+l- distribute-neg-frac
exp-diff
associate-+l+ associate-+r+ log-rec sqrt-unprod asin-acos
distribute-frac-neg sub-div acos-neg associate--r- distribute-rgt-out
sin-sum cube-unmult tanh-undef rem-exp-log
remove-posit16 cos-mult associate-+r- tanh-def difference-cubes rem-square-sqrt sin-diff distribute-rgt1-in

regimes11.8s

Accuracy

Total 57.8b remaining (33.1%)

Threshold costs 4.6b (2.6%)

7.6b43.3%Quadratic roots, narrow range
7.6b43.6%Cubic critical, narrow range
6.6b0%Quadratic roots, medium range
5.9b12.5%Cubic critical, medium range
5.0b61.8%Equirectangular approximation to distance on a great circle

localize4.9s

end1.0ms