Details

sample9.9m (58.5%)

Algorithm

78×

intervals

Results

5.4m	36130×	body	10240	exit
1.8m	44174×	body	1280	valid
41.1s	30014×	body	640	valid
30.4s	203789×	body	80	valid
22.0s	152223×	body	80	nan
21.4s	27831×	body	320	valid
13.3s	36179×	body	160	valid
12.3s	174649×	pre	80	true
2.7s	2992×	body	2560	valid
1.9s	8098×	body	160	nan
912.0ms	4179×	pre	10240	exit
385.0ms	232×	body	5120	valid
3.0ms	2×	body	640	nan

simplify3.4m (20.0%)

prune1.8m (10.8%)

series54.5s (5.4%)

Calls

480 calls:

1.7s	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (cos delta) (+ (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (* (cos phi1) (sin phi1)) (cos theta)) (sin delta))))) (log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
1.3s	(cbrt (* (* (- (cos delta) (* (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)))))))) (log (/ (exp (cos delta)) (exp (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))))
981.0ms	(sqrt (+ (/ (* (* (cos (/ (+ phi1 phi2) 2)) (* (+ lambda2 lambda1) (- lambda1 lambda2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (+ lambda1 lambda2)) (* (- phi1 phi2) (- phi1 phi2))))
613.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
572.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

regimes21.2s (2.1%)

Accuracy

Total 68.7b remaining (32.8%)

Threshold costs 5.5b (2.6%)

11.8b	35.9%	Equirectangular approximation to distance on a great circle
8.0b	42.2%	Quadratic roots, narrow range
7.8b	41.8%	Cubic critical, narrow range
6.8b	0%	Quadratic roots, medium range
6.7b	0%	Cubic critical, medium range

rewrite20.0s (2.0%)

Algorithm

144×	rewrite-expression-head

Calls

480 calls:

682.0ms	(/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a)))
603.0ms	(cbrt (/ (/ (* (* (* (* 9/4 (/ a (/ b c))) (/ a (/ b c))) (/ a (/ b c))) -3/2) 27) (* a (* a a))))
527.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cbrt (* (* (cos (/ (+ phi1 phi2) 2)) (cos (/ (+ phi1 phi2) 2))) (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
504.0ms	(* (- (/ (- (/ m v) (/ (* m (* m m)) v)) (+ 1 m)) 1) (- 1 m))
459.0ms	(* (* (/ (* -1/2 (* a c)) (* a b)) (/ (* -1/2 (* a c)) (* a b))) (/ (* -1/2 (* a c)) (* a b)))

Rules

8269×	`add-exp-log`
6793×	`add-cbrt-cube`
5269×	`times-frac`
5003×	`*-un-lft-identity`
4713×	`add-sqr-sqrt`
4067×	`prod-exp`
3312×	`add-cube-cbrt`
3299×	`cbrt-unprod`
2721×	`div-exp`
2016×	`cbrt-undiv`
1498×	`associate-*l/`
1225×	`pow1`
1175×	`flip--`
1174×	`flip3--`
1059×	`frac-times`
788×	`add-log-exp`
700×	`pow-exp`
698×	`associate-r`
696×	`associate-l`
687×	`frac-add`
678×	`sqrt-div`
648×	`difference-of-squares`
549×	`associate-/r*`
533×	`associate-*r/`
480×	`insert-posit16`
468×	`distribute-lft-out`
463×	`associate-/l*`
456×	`cbrt-div`
413×	`div-inv`
391×	`cbrt-prod`
352×	`sqrt-prod` `pow-to-exp`
342×	`log-prod`
312×	`cos-mult`
287×	`associate-/r/`
264×	`distribute-lft-out--`
244×	`pow-prod-down`
220×	`flip-+`
219×	`flip3-+`
165×	`1-exp` `rec-exp`
162×	`unswap-sqr`
118×	`*-commutative`
110×	`associate-/l/`
108×	`frac-2neg` `clear-num`
107×	`swap-sqr`
103×	`sub-neg`
90×	`pow-prod-up`
89×	`diff-log`
87×	`difference-of-sqr-1`
83×	`sum-log`
76×	`unpow-prod-down` `log-pow`
61×	`tan-quot`
58×	`pow1/3`
56×	`pow-plus`
52×	`pow-sqr`
50×	`distribute-rgt-in` `distribute-lft-in`
49×	`rem-log-exp` `log-div`
38×	`pow2`
37×	`+-commutative` `distribute-rgt-out`
35×	`sqrt-pow1` `pow1/2`
34×	`div-sub`
33×	`rem-sqrt-square`
31×	`sin-cos-mult`
27×	`distribute-rgt-out--` `exp-prod`
25×	`frac-sub`
24×	`pow-flip`
20×	`associate-+r+` `sqr-pow`
19×	`inv-pow`
17×	`sin-diff`
16×	`associate--l+`
15×	`sin-mult`
14×	`cos-diff`
13×	`cos-sum`
12×	`associate--r+`
10×	`exp-sum` `acos-asin`
9×	`distribute-rgt1-in`
8×	`rem-exp-log`
7×	`associate-+l+` `pow3` `un-div-inv`
6×	`associate--l-` `sin-sum` `pow-unpow` `log-rec` `pow-pow`
5×	`exp-diff` `cube-unmult` `associate--r-`
4×	`remove-posit16` `associate-+r-` `associate-+l-` `rem-cbrt-cube`
3×	`distribute-frac-neg` `exp-to-pow` `acos-neg`
1×	`tanh-undef` `tanh-def` `difference-cubes` `asin-acos` `sub-div`

Details

sample9.9m (58.5%)

simplify3.4m (20.0%)

prune1.8m (10.8%)

series54.5s (5.4%)

regimes21.2s (2.1%)

rewrite20.0s (2.0%)

localize7.0s (0.7%)

bsearch5.9s (0.6%)

end2.0ms (0.0%)