Details

sample257.0ms

Algorithm

intervals

Results

184.0ms	145×	body	1280	valid
42.0ms	58×	body	640	valid
10.0ms	21×	body	320	valid
4.0ms	26×	body	80	valid
2.0ms	6×	body	160	valid

simplify33.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	71	24
4	74	24
done	74	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))
1.6b	(sin (- lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`cos-diff`
2×	`sub-neg` `cos-sum` `sin-sum` `*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `sin-cos-mult` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series168.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (cos phi1) (sin phi2))
87.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))
20.0ms	(sin (- lambda1 lambda2))

simplify1.7s

Counts

71 → 71

Iterations

Useful iterations: 3 (367.0ms)

Iter	Nodes	Cost
0	128	709
1	291	697
2	1000	601
3	3149	599
done	5000	599

prune307.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
1.6b	(cos (- lambda1 lambda2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`associate-l`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`cos-diff` `*-commutative`
2×	`cos-sum` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/` `sin-neg` `distribute-rgt-neg-out` `sin-cos-mult`

Counts

4 → 68

Calls

4 calls:

5.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))

series194.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (cos lambda1) (sin (- lambda2)))
41.0ms	(* (cos phi1) (sin phi2))
86.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

simplify417.0ms

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	150	804
1	345	790
2	1219	678