Details

sample258.0ms

Algorithm

intervals

Results

187.0ms	145×	body	1280	valid
40.0ms	59×	body	640	valid
9.0ms	22×	body	320	valid
3.0ms	25×	body	80	valid
1.0ms	5×	body	160	valid

simplify39.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	27	24
2	45	24
3	70	24
4	72	24
done	72	24

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))
5.1b	(sin (- lambda1 lambda2))

rewrite28.0ms

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` `sin-cos-mult`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-*l/` `sin-diff` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
12.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

series170.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))
22.0ms	(sin (- lambda1 lambda2))

simplify3.9s

Counts

72 → 72

Iterations

Useful iterations: 3 (636.0ms)

Iter	Nodes	Cost
0	114	718
1	254	706
2	824	610
3	2333	608
4	4419	608
done	5000	608

prune321.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 8.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.2b	(* (sin phi1) (cos phi2))
0.2b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.9b	(cos (- lambda1 lambda2))

rewrite24.0ms

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` `sin-cos-mult` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*l/`

Counts

4 → 68

Calls

4 calls:

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

series199.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos phi1) (sin phi2))
49.0ms	(* (sin phi1) (cos phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify3.1s

Counts

80 → 80

Iterations

Useful iterations: 3 (732.0ms)

Iter	Nodes	Cost
0	134	782
1	303	769
2	997	661
3	2819	659
done	5001	659

prune410.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`associate-r`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
6×	`pow-prod-down` `prod-exp` `sin-cos-mult` `cbrt-unprod`
5×	`sin-mult`
4×	`frac-times` `associate-r/` `cos-mult` `-commutative` `add-log-exp`
3×	`unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `frac-sub` `flip--` `sub-div`
1×	`associate-*l/` `sin-neg` `distribute-rgt-neg-out`

Counts

4 → 88

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin phi1) (cos phi2))
6.0ms	(* (sin lambda1) (sin (- lambda2)))
25.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

series330.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (cos phi1) (sin phi2))
42.0ms	(* (sin phi1) (cos phi2))
56.0ms	(* (sin lambda1) (sin (- lambda2)))
185.0ms	(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))

simplify968.0ms

Counts

100 → 100

Iterations

Useful iterations: done (965.0ms)

Iter	Nodes	Cost
0	195	1445
1	480	1398
2	1774	1196
done	5000	1194

prune567.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-exp-log` `add-cbrt-cube`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
5×	`sin-cos-mult`
4×	`*-commutative` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 88

Calls

4 calls:

4.0ms	(* (sin phi1) (cos phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
15.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
16.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin phi1) (cos phi2))
50.0ms	(* (sin lambda1) (sin lambda2))
101.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
113.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify919.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (146.0ms)

Iter	Nodes	Cost
0	151	1238
1	387	1212
2	1411	952
done	5000	952

prune455.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes427.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	44
1	35	44
done	35	44

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.3s	4646×	body	1280	valid
1.4s	1891×	body	640	valid
277.0ms	572×	body	320	valid
105.0ms	695×	body	80	valid
62.0ms	196×	body	160	valid