Details

sample4.8m (63.3%)

Algorithm
intervals
Results
2.8m10285×body1280valid
1.2m5785×body640valid
15.6s19497×body80valid
14.8s2342×body320valid
5.1s22423×pre80true
3.0s1016×body160valid
172.0ms11×body2560valid

simplify1.6m (20.6%)

series28.3s (6.2%)

Calls

61 calls:

5.2s
(+ (pow (cos phi1) 3) (pow (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))
2.6s
(cbrt (* (- m) (- (/ (* m (- 1.0 m)) v) 1.0)))
2.1s
(* (cbrt (* (- m) (- (/ (* m (- 1.0 m)) v) 1.0))) (cbrt (* (- m) (- (/ (* m (- 1.0 m)) v) 1.0))))
1.9s
(cbrt (* (- m) (- (/ (* m (- 1.0 m)) v) 1.0)))
1.7s
(cbrt (* (- m) (- (/ (* m (- 1.0 m)) v) 1.0)))

prune23.9s (5.2%)

regimes11.4s (2.5%)

Accuracy

Total 0.7b remaining (6.7%)

Threshold costs 0.7b (6.7%)

0.4b0%Spherical law of cosines
0.2b0%Midpoint on a great circle
0.1b0%Trigonometry A
0.1b0%b parameter of renormalized beta distribution

rewrite7.6s (1.7%)

Algorithm
16×rewrite-expression-head
Calls

61 calls:

725.0ms
(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
567.0ms
(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))
563.0ms
(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
382.0ms
(/ (* (sqrt e) (* (sqrt e) (sin v))) (+ 1.0 (* e (cos v))))
329.0ms
(log (exp (* (sin lambda1) (sin (- lambda2)))))
Rules
290×add-sqr-sqrt
242×*-un-lft-identity
214×add-cube-cbrt
173×add-exp-log
171×add-cbrt-cube
149×times-frac
135×pow1
110×associate-*r*
89×associate-*l*
79×add-log-exp
53×associate-*r/
43×cbrt-unprod prod-exp
38×flip-- flip3--
37×associate-/r*
35×pow-prod-down
25×*-commutative
24×unswap-sqr
23×sub-neg
22×distribute-rgt-in distribute-lft-in
19×associate-/l* cbrt-undiv div-exp
18×cbrt-div frac-times
15×div-inv
14×cos-mult
13×distribute-lft-out-- difference-of-squares
11×flip-+ flip3-+ log-pow
10×associate-/l/ associate-+r+ exp-prod
cos-diff frac-2neg pow1/3 associate-*l/ associate-/r/ clear-num
sin-mult
sqrt-prod cbrt-prod
pow-unpow acos-asin log-prod cos-sum
sin-neg frac-add +-commutative sum-log distribute-rgt-neg-out
unpow-prod-down associate-+l+ exp-neg cube-prod swap-sqr log-div
distribute-rgt-neg-in cube-div rem-cube-cbrt distribute-lft-neg-out distribute-lft-neg-in pow-exp pow-pow diff-log
exp-diff sin-sum sqr-pow pow-prod-up pow-to-exp pow-sqr unpow3 cube-mult sub-div associate--r- frac-sub associate--l+ rem-log-exp
rem-exp-log pow2 unsub-neg distribute-lft-out pow-plus distribute-rgt-out div-sub neg-mul-1 sum-cubes exp-to-pow sin-diff log-rec

localize2.9s (0.6%)

bsearch2.0ms (0.0%)

end1.0ms (0.0%)