Details

sample7.4m (44.4%)

Algorithm
78×intervals
Results
4.4m33337×body10240exit
1.3m43487×body1280valid
27.6s30724×body640valid
18.2s203273×body80valid
13.2s151837×body80nan
10.8s27892×body320valid
8.3s36078×body160valid
7.7s170932×pre80true
2.2s3103×body2560valid
1.1s7662×body160nan
460.0ms4163×pre10240exit
167.0ms223×body5120valid

simplify5.0m (30.0%)

prune1.8m (10.9%)

series1.1m (6.4%)

Calls

459 calls:

7.3s
(sqrt (+ (* (* (- lambda1 lambda2) (+ (log (* (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (exp (cos (/ (+ phi1 phi2) 2.0)))))) (log (cbrt (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
4.1s
(cbrt (* (* (log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))
3.8s
(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))) (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))))
2.1s
(cbrt (* (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
2.1s
(cbrt (* (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (+ (* (cos delta) (cos delta)) (+ (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (* (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))

rewrite50.8s (5.1%)

Algorithm
144×rewrite-expression-head
Calls

459 calls:

20.0s
(- (* (* (* (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))) (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)))) (* (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))) (* (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1)) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))))) (/ (* (/ x0 (- 1.0 x1)) (/ x0 (- 1.0 x1))) (- 1.0 x1))) (* (* (* x0 x0) (* (* (* x0 x0) (* x0 x0)) (* (* x0 x0) (* x0 x0)))) (* (* (* x0 x0) (* x0 x0)) (* (* x0 x0) (* x0 x0)))))
2.4s
(- (/ (/ (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
1.8s
(* (* (* (* x0 x0) (* x0 x0)) (* x0 x0)) (* (* (* x0 x0) (* x0 x0)) (* x0 x0)))
909.0ms
(/ (+ (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (* (cos lambda2) (* (cos lambda1) (cos phi2))) (* (cos lambda2) (* (cos lambda1) (cos phi2))))) (* (cos phi1) (* (cos phi1) (cos phi1)))) (+ (* (cos phi1) (cos phi1)) (* (- (* (cos lambda2) (* (cos lambda1) (cos phi2))) (cos phi1)) (* (cos lambda2) (* (cos lambda1) (cos phi2))))))
891.0ms
(cbrt (* (* (sin (/ (- lambda1 lambda2) 2.0)) (* (* (cbrt (sin (/ (- lambda1 lambda2) 2.0))) (cbrt (sin (/ (- lambda1 lambda2) 2.0)))) (cbrt (sin (/ (- lambda1 lambda2) 2.0))))) (sin (/ (- lambda1 lambda2) 2.0))))
Rules
129798×pow1
75335×pow-prod-up
26325×pow-plus
25489×pow-prod-down
24705×pow-sqr
14198×pow2
13940×times-frac
10316×*-un-lft-identity
9361×sqrt-prod
8129×add-sqr-sqrt
6925×add-cube-cbrt
3755×add-exp-log
3087×add-cbrt-cube
1833×prod-exp
1495×cbrt-unprod
1346×distribute-lft-out
1007×associate-/l*
851×sqrt-div
815×frac-times
769×div-exp
763×associate-*l/
756×associate-*r*
743×flip--
742×flip3--
709×add-log-exp
688×frac-add
591×associate-*l*
571×associate-*r/
514×div-inv
481×associate-/r*
473×cbrt-undiv
459×flip-+
458×flip3-+
411×associate-/r/
377×difference-of-squares
307×distribute-lft-out--
298×cbrt-div
269×pow-exp
268×cbrt-prod
239×sin-mult
212×cos-mult
206×swap-sqr
188×pow-to-exp
163×unswap-sqr
160×log-prod
123×frac-2neg clear-num exp-prod
114×pow3
109×sub-neg
108×*-commutative
94×associate-/l/
89×diff-log
57×unpow-prod-down log-pow
55×pow1/3
53×distribute-rgt-neg-in
49×frac-sub
47×sum-log
46×log-div
44×distribute-rgt-in distribute-lft-in
43×sqrt-pow1 pow1/2
34×div-sub
32×distribute-lft-neg-in
30×rem-sqrt-square
28×+-commutative
25×distribute-rgt-out
22×rem-log-exp
20×1-exp rec-exp
19×associate--l+
18×tan-quot
16×cos-diff
15×cos-sum
14×sin-diff
13×cube-unmult associate--r+
12×neg-mul-1 distribute-rgt1-in
11×neg-sub0 sqr-pow
10×exp-diff associate-+r+
associate--l- pow-unpow acos-asin
sin-cos-mult exp-neg
associate-+l+ exp-sum associate--r-
distribute-lft-neg-out sin-sum pow-flip neg-log sum-cubes inv-pow
associate-+r- pow-pow un-div-inv rem-cbrt-cube
distribute-rgt-neg-out distribute-frac-neg distribute-neg-frac asin-acos rem-exp-log acos-neg
distribute-lft1-in rem-cube-cbrt pow-div associate-+l- sqr-cos
quot-tan cube-prod unsub-neg unpow3 sqrt-unprod tanh-undef cube-mult tanh-def difference-cubes rem-square-sqrt cube-div

regimes23.8s (2.4%)

Accuracy

Total 63.2b remaining (30%)

Threshold costs 6.3b (3%)

7.5b45.2%Quadratic roots, narrow range
7.4b45.8%Cubic critical, narrow range
6.9b0%Quadratic roots, medium range
6.3b61.9%Equirectangular approximation to distance on a great circle
6.3b44.2%Quotient of products

localize7.6s (0.8%)

bsearch985.0ms (0.1%)

end1.0ms (0.0%)