Details

sample275.0ms

Algorithm

intervals

Results

198.0ms	146×	body	1280	valid
48.0ms	67×	body	640	valid
8.0ms	16×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	7×	body	160	valid

simplify28.0ms

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: 11.7b

localize28.0ms

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))

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))
10.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms	(sin (- lambda1 lambda2))
5.0ms	(cos (- 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)))
20.0ms	(sin (- lambda1 lambda2))
18.0ms	(cos (- lambda1 lambda2))

simplify1.6s

Counts

71 → 71

Iterations

Useful iterations: 3 (573.0ms)

Iter	Nodes	Cost
0	128	709
1	286	697
2	916	601
3	3311	599
done	5000	599

prune328.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

localize34.0ms

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))

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

Counts

4 → 67

Calls

4 calls:

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

series189.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos lambda1) (sin lambda2))
44.0ms	(* (cos phi1) (sin phi2))
86.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
16.0ms	(cos (- lambda1 lambda2))

simplify1.9s

Counts

79 → 79

Iterations

Useful iterations: 3 (664.0ms)

Iter	Nodes	Cost
0	145	773
1	331	760
2	1076	652
3	3850	650
done	5001	650

prune432.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

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)))

rewrite38.0ms

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:

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos phi1) (sin phi2))
47.0ms	(* (sin lambda1) (sin lambda2))
94.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
109.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify540.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (130.0ms)

Iter	Nodes	Cost
0	165	1229
1	419	1203
2	1507	943
done	5001	943

prune519.0ms

Pruning

12 alts after pruning (12 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)) (sin lambda1))
0.2b	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
0.2b	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

rewrite55.0ms

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:

4.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
26.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
13.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
65.0ms	(* (* (sin phi1) (cos phi2)) (sin lambda1))
102.0ms	(* (* (* (sin phi1) (cos phi2)) (sin lambda1)) (sin lambda2))
110.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify667.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (170.0ms)

Iter	Nodes	Cost
0	166	1239
1	419	1213
2	1729	947
done	5001	947

prune630.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

regimes427.0ms

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	29	47
1	40	47
done	40	47

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.3s	4640×	body	1280	valid
1.5s	1986×	body	640	valid
273.0ms	564×	body	320	valid
87.0ms	623×	body	80	valid
57.0ms	187×	body	160	valid