Details

sample10.6m (78.9%)

Algorithm
78×intervals
Results
8.1m51433×body10240exit
58.3s44179×body1280valid
20.1s30315×body640valid
14.5s204702×body80valid
10.7s152738×body80nan
9.4s27515×body320valid
7.3s189961×pre80true
6.0s36369×body160valid
1.9s2910×body2560valid
566.0ms7816×body160nan
454.0ms8075×pre80false
428.0ms4048×pre10240exit
249.0ms273×body5120valid
2.0msbody640nan

series59.6s (7.4%)

Calls

515 calls:

4.9s
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) 3)) (+ (* (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (- (* (cos phi2) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))) (cos phi1))) (* (cos phi1) (cos phi1))))
1.6s
(- (/ x (+ x 1.0)) (/ (/ (+ x 1.0) (+ (sqrt x) (sqrt 1.0))) (- (sqrt x) (sqrt 1.0))))
769.0ms
(exp (log (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))))))
663.0ms
(/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))))
637.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

prune52.8s (6.6%)

rewrite31.1s (3.9%)

Algorithm
146×rewrite-expression-head
Calls

515 calls:

5.0s
(- (/ (/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) 1.0)
751.0ms
(- (- (/ (- 1.0) (pow x 2)) (/ 3.0 x)) (/ 3.0 (pow x 3)))
704.0ms
(/ (- (pow (/ 1.0 (+ x 1.0)) 3) (pow (/ 1.0 (- x 1.0)) 3)) (+ (* (/ 1.0 (- x 1.0)) (+ (/ 1.0 (- x 1.0)) (/ 1.0 (+ x 1.0)))) (* (/ 1.0 (+ x 1.0)) (/ 1.0 (+ x 1.0)))))
703.0ms
(* (* (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))) (cbrt (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0)))))
519.0ms
(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
8143×times-frac
7806×*-un-lft-identity
7158×add-sqr-sqrt
4432×add-cube-cbrt
2686×add-exp-log
1724×add-cbrt-cube
1594×sqrt-prod
1206×associate-*r*
1132×distribute-lft-out--
1085×pow1
1037×associate-*l/
1023×flip--
1007×unpow-prod-down
1001×flip3--
952×difference-of-squares
876×associate-/l*
825×prod-exp
823×div-exp
812×add-log-exp
682×frac-times
677×cbrt-prod
674×distribute-lft-out
669×cube-prod
660×associate-/r*
650×frac-add
618×sqrt-div
472×associate-*l*
470×associate-*r/
413×cbrt-div
409×div-inv
398×cbrt-undiv
383×cbrt-unprod
356×distribute-rgt-neg-in
343×associate-/r/
326×pow-exp
316×flip-+
294×flip3-+
255×sqr-pow
241×pow-to-exp
228×pow-prod-down
214×unswap-sqr
153×log-prod
127×swap-sqr
124×clear-num frac-2neg
120×sub-neg
119×associate-/l/
108×distribute-lft-neg-in pow1/3
106×*-commutative
95×diff-log log-div
71×exp-diff
67×unpow3 cube-mult
65×1-exp
62×sum-log
61×div-sub
60×pow-unpow log-pow
59×exp-prod
53×unpow2
45×+-commutative rec-exp
43×pow-prod-up
42×neg-sub0
41×distribute-rgt-in distribute-lft-in sqrt-pow1
39×pow1/2 rem-sqrt-square
36×exp-sum
35×neg-mul-1
34×cube-div
31×pow-sqr associate-+l- associate--l+
29×sin-mult
28×distribute-rgt-out
27×pow-plus cos-mult
26×frac-sub
25×associate-+r+
24×pow-pow
23×neg-log
18×associate--l- rem-log-exp
17×pow2
15×cos-diff sin-diff
14×pow-flip
13×cos-sum rem-cube-cbrt
12×tan-quot distribute-rgt-neg-out
11×sin-sum rem-cbrt-cube
10×associate-+l+
sin-cos-mult rem-exp-log inv-pow acos-asin associate-+r-
distribute-frac-neg
sub-div
difference-cubes distribute-lft1-in pow3
sin-neg sum-cubes unsub-neg
acos-neg associate--r- associate--r+
un-div-inv pow-sub distribute-neg-frac pow-neg tanh-def
distribute-neg-out unpow1/3 sqrt-unprod sqr-sin tanh-undef asin-acos

simplify13.0s (1.6%)

regimes9.4s (1.2%)

Accuracy

Total 26.4b remaining (20.5%)

Threshold costs 6.4b (5%)

4.9b54.7%Quotient of products
4.8b83.1%Cubic critical
3.5b74.5%Equirectangular approximation to distance on a great circle
3.3b87.9%Quadratic roots, full range
1.3b0%2-ancestry mixing, positive discriminant

localize3.3s (0.4%)

bsearch702.0ms (0.1%)

end1.0ms (0.0%)