Details

simplify4.1m (52.3%)

sample1.9m (24.6%)

Algorithm
77×intervals
Results
34.0s15913×body10240exit
33.7s43972×body1280valid
10.8s29783×body640valid
6.8s202058×body80valid
4.5s27684×body320valid
4.4s152509×body80nan
2.9s36124×body160valid
2.5s151934×pre80true
719.0ms2964×body2560valid
369.0ms8106×body160nan
338.0ms4022×pre10240exit
89.0ms8332×pre80false
51.0ms208×body5120valid

prune44.6s (9.4%)

series38.4s (8.1%)

Calls

477 calls:

746.0ms
(/ (+ (pow (cos phi1) 3) (pow (* (cos phi2) (* (cos lambda1) (cos lambda2))) 3)) (+ (* (cos phi1) (cos phi1)) (* (* (cos phi2) (* (cos lambda1) (cos lambda2))) (- (* (cos phi2) (* (cos lambda1) (cos lambda2))) (cos phi1)))))
688.0ms
(exp (log (sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))))
684.0ms
(sqrt (+ (* (pow (cbrt (cos (/ (+ phi1 phi2) 2.0))) 6) (* (- lambda1 lambda2) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
521.0ms
(exp (* (cbrt (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0))))) (cbrt (log (log (+ (* 1/2 (pow x 2)) (+ x 2.0)))))))
455.0ms
(/ (* (+ (pow (* -1/6 (/ (* x x) 1.0)) 3) 1) (/ x (sqrt 1.0))) (+ (* (* -1/6 (/ (* x x) 1.0)) (* -1/6 (/ (* x x) 1.0))) (- (* 1 1) (* (* -1/6 (/ (* x x) 1.0)) 1))))

rewrite15.7s (3.3%)

Algorithm
143×rewrite-expression-head
Calls

477 calls:

590.0ms
(* (- (/ 1 (/ (/ v m) (- 1.0 m))) 1.0) m)
449.0ms
(log (exp (- (/ (pow x0 3) (pow (- 1.0 x1) 6)) (pow x0 3))))
428.0ms
(/ (* (+ (pow (* -1/6 (/ (* x x) 1.0)) 3) 1) (/ x (sqrt 1.0))) (+ (* (* -1/6 (/ (* x x) 1.0)) (* -1/6 (/ (* x x) 1.0))) (- (* 1 1) (* (* -1/6 (/ (* x x) 1.0)) 1))))
253.0ms
(- (/ x0 (* (- 1.0 x1) (- 1.0 x1))) x0)
193.0ms
(- (/ x (+ x 1.0)) (+ (* (/ (+ x 1.0) (- (pow x 3) (pow 1.0 3))) (* x x)) (* (* 1.0 (* (+ x 1.0) (/ (sqrt (+ x 1.0)) (+ (* x x) (* 1.0 (+ x 1.0)))))) (/ (sqrt (+ x 1.0)) (- x 1.0)))))
Rules
7978×times-frac
7368×add-sqr-sqrt
7028×*-un-lft-identity
4056×add-cube-cbrt
2073×add-exp-log
1750×add-cbrt-cube
1659×difference-of-squares
961×pow1
905×unpow-prod-down
875×associate-*r*
863×distribute-lft-out--
813×associate-*l*
776×flip--
775×flip3--
766×associate-/r* cube-prod
719×add-log-exp
594×distribute-lft-out
590×cbrt-prod
573×associate-*l/
563×div-exp
552×sqrt-prod
536×sqr-pow
525×associate-/l*
492×prod-exp
459×associate-*r/
452×frac-times
443×div-inv
420×cbrt-undiv
408×cbrt-unprod
388×sqrt-div
370×frac-add
334×associate-/r/
317×log-prod
194×unswap-sqr
184×flip-+
183×flip3-+
181×pow-prod-down
155×distribute-rgt-neg-in
132×exp-prod
126×log-pow
117×log-div
114×clear-num frac-2neg
113×exp-sum
110×*-commutative
102×swap-sqr
101×cbrt-div
98×associate-/l/ sub-neg
72×exp-diff
66×diff-log
65×distribute-rgt-in distribute-lft-in
57×pow-unpow sum-log
56×pow1/3
49×1-exp
48×div-sub
47×pow1/2 sqrt-pow1
45×rec-exp
42×difference-cubes
40×+-commutative
38×unpow3 cube-mult
36×frac-sub
35×pow-exp
33×rem-log-exp
30×rem-sqrt-square
29×pow-to-exp
28×pow-prod-up distribute-rgt-out
26×associate--r+
25×sin-mult cos-mult
24×pow-sqr
23×pow-pow
22×sin-diff
18×tan-quot
16×cos-diff
15×neg-sub0 cos-sum
14×sin-sum pow-plus
13×cube-div associate--l+ pow2
12×rem-cube-cbrt pow-flip
11×sin-cos-mult inv-pow
10×neg-log asin-acos distribute-rgt-neg-out associate-+l-
8×associate--l- associate-+r+ acos-asin
7×rem-exp-log
6×distribute-frac-neg sin-neg unpow2
5×sum-cubes distribute-lft1-in associate--r-
4×associate-+r-
3×acos-neg sub-div exp-to-pow rem-cbrt-cube
2×un-div-inv sqrt-unprod exp-neg unsub-neg rem-square-sqrt pow-neg log-rec
1×sin-asin sqr-sin pow-sub tanh-undef tanh-def

regimes8.4s (1.8%)

Accuracy

Total 50.2b remaining (33.5%)

Threshold costs 5.4b (3.6%)

11.0b39.9%Equirectangular approximation to distance on a great circle
7.5b46.3%Cubic critical, narrow range
6.1b11.9%Quadratic roots, medium range
6.0b44.9%Quotient of products
4.6b83.5%Quadratic roots, full range

localize2.2s (0.5%)

bsearch883.0ms (0.2%)

end1.0ms (0.0%)