Details

sample272.0ms

Algorithm

intervals

Results

191.0ms	146×	body	1280	valid
47.0ms	67×	body	640	valid
7.0ms	16×	body	320	valid
2.0ms	20×	body	80	valid
2.0ms	7×	body	160	valid

simplify29.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(sin (- lambda1 lambda2))
3.3b	(cos (- lambda1 lambda2))

rewrite27.0ms

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

series173.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos phi1) (sin phi2))
89.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
21.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify3.3s

Counts

71 → 71

Iterations

Useful iterations: 3 (496.0ms)

Iter	Nodes	Cost
0	128	709
1	286	697
2	906	601
3	2682	599
4	4879	599
done	5000	599

prune326.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos lambda1) (sin (- lambda2)))
0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.3b	(cos (- lambda1 lambda2))

rewrite26.0ms

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:

6.0ms	(* (cos lambda1) (sin (- lambda2)))
4.0ms	(* (cos phi1) (sin phi2))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
5.0ms	(cos (- lambda1 lambda2))

series205.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos lambda1) (sin (- lambda2)))
48.0ms	(* (cos phi1) (sin phi2))
90.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify1.9s

Counts

80 → 80

Iterations

Useful iterations: 3 (599.0ms)

Iter	Nodes	Cost
0	150	804
1	338	790
2	1098	678
3	3252	676
done	5000	676

prune449.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin 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)))

rewrite41.0ms

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*`
4×	`*-commutative` `sin-cos-mult` `add-log-exp`
3×	`sin-mult`
2×	`frac-times` `associate-r/` `associate-l/` `cos-mult` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

6.0ms	(* (cos phi1) (sin phi2))
4.0ms	(* (sin lambda1) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
44.0ms	(* (sin lambda1) (sin lambda2))
98.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
112.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify540.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (133.0ms)

Iter	Nodes	Cost
0	165	1229
1	419	1203
2	1499	943
done	5000	943

prune734.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

6.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
26.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
14.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series312.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos phi1) (sin phi2))
67.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
95.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
109.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify701.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (173.0ms)

Iter	Nodes	Cost
0	166	1239
1	419	1213
2	1713	947
done	5001	947

prune441.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes441.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	48
1	43	48
done	43	48

end0.0ms

sample8.4s

Algorithm

intervals

Results

6.2s	4640×	body	1280	valid
1.5s	1986×	body	640	valid
284.0ms	564×	body	320	valid
104.0ms	623×	body	80	valid
67.0ms	187×	body	160	valid