Details

sample5.4m (57.8%)

Algorithm
10×intervals
Results
2.8m10285×body1280valid
1.2m5785×body640valid
19.5s6074×body160valid
18.6s21293×body80valid
15.6s3744×body320valid
9.0s8707×body80nan
8.6s39386×pre80true
172.0ms11×body2560valid

simplify2.2m (23.8%)

prune37.4s (6.7%)

series37.4s (6.7%)

Calls

77 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)))

rewrite12.3s (2.2%)

Algorithm
20×rewrite-expression-head
Calls

77 calls:

1.1s
(/ (/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0)))))) (* 2.0 a))
725.0ms
(exp (acos (+ (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))) (* (sin phi1) (sin phi2)))))
652.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (- b) (sqrt (/ (- (pow b 4) (* (* (* a c) 4.0) (* (* a c) 4.0))) (+ (* b b) (* (* a c) 4.0))))))
567.0ms
(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m))
563.0ms
(/ (* e (sin v)) (+ 1.0 (* e (cos v))))
Rules
1093×times-frac
771×add-sqr-sqrt
696×*-un-lft-identity
586×add-exp-log
496×add-cube-cbrt
392×add-cbrt-cube
266×pow1
250×div-exp
158×prod-exp
115×difference-of-squares
111×add-log-exp associate-*r*
108×associate-/l* cbrt-unprod cbrt-undiv
101×pow-prod-down
96×associate-/r*
93×distribute-lft-out--
90×associate-*l*
77×div-inv
73×associate-/r/
67×flip3-- flip--
60×sqrt-prod
53×associate-*r/
46×distribute-rgt-neg-in
45×1-exp
27×sub-neg
26×*-commutative
24×unswap-sqr
22×distribute-rgt-in distribute-lft-in
21×associate-/l/
18×cbrt-div clear-num rec-exp frac-times frac-2neg
16×flip-+ flip3-+
14×cos-mult
11×pow-prod-up pow-sqr log-pow
10×associate-+r+ exp-prod
cos-diff pow1/3 associate-*l/ diff-log
unpow-prod-down sin-mult
distribute-lft-out sum-log cbrt-prod
pow-unpow sqr-pow +-commutative acos-asin log-prod cos-sum
sin-neg frac-add swap-sqr distribute-rgt-neg-out
exp-neg associate-+l+ pow-plus cube-prod neg-sub0 log-div
cube-div rem-cube-cbrt distribute-lft-neg-in distribute-lft-neg-out neg-log pow-exp div-sub pow-pow
exp-diff unpow3 sqrt-div associate--l- sin-sum pow-to-exp pow2 cube-mult sub-div associate--r- frac-sub associate-+l- associate--l+ rem-log-exp
pow1/2 rem-sqrt-square rem-exp-log unsub-neg distribute-rgt-out neg-mul-1 sum-cubes exp-to-pow sqrt-pow1 sin-diff log-rec

regimes12.2s (2.2%)

Accuracy

Total 1.1b remaining (6.7%)

Threshold costs 1.1b (6.7%)

0.4b0%Quadratic roots, medium range
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

localize3.6s (0.6%)

end6.0ms (0.0%)

bsearch2.0ms (0.0%)