Details

sample270.0ms

Algorithm

intervals

Results

201.0ms	151×	body	1280	valid
40.0ms	57×	body	640	valid
8.0ms	18×	body	320	valid
3.0ms	22×	body	80	valid
2.0ms	8×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	15
1	46	15
2	71	15
3	77	15
4	77	15

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.6b

Counts

2 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))
3.6b	(sin (- lambda1 lambda2))

rewrite36.0ms

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:

8.0ms	(* (cos phi1) (sin phi2))
11.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
7.0ms	(cos (- lambda1 lambda2))
7.0ms	(sin (- lambda1 lambda2))

series180.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos phi1) (sin phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
20.0ms	(cos (- lambda1 lambda2))
31.0ms	(sin (- lambda1 lambda2))

simplify106.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	286	430
1	1077	367
2	4907	367
3	5001	367

prune329.0ms

Filtered

71 candidates to 50 candidates (70.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 6.5b

Counts

72 → 13

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
0.2b	(* (cos phi1) (sin phi2))
0.3b	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
3.5b	(cos (- lambda1 lambda2))

rewrite20.0ms

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` `add-log-exp`
5×	`cos-diff`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`distribute-rgt-in` `sub-neg` `cos-sum` `distribute-lft-in` `*-commutative` `associate--r+`
1×	`flip3--` `diff-log` `associate-*l/` `sin-cos-mult` `flip--` `unswap-sqr`

Counts

4 → 63

Calls

4 calls:

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (* (cos phi1) (sin phi2)) (* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2))))
42.0ms	(* (cos phi1) (sin phi2))
88.0ms	(* (* (sin phi1) (cos phi2)) (cos (- lambda1 lambda2)))
17.0ms	(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	318	598
1	1315	539
2	5002	539

prune375.0ms

Filtered

75 candidates to 53 candidates (70.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	6	6	12
Picked	1	0	1
Done	0	0	0
Total	76	12	88

Merged error: 0.1b

Counts

88 → 12

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)))

rewrite32.0ms

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))
5.0ms	(* (sin lambda1) (sin lambda2))
9.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
12.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (cos phi1) (sin phi2))
44.0ms	(* (sin lambda1) (sin lambda2))
97.0ms	(* (* (sin phi1) (cos phi2)) (* (sin lambda1) (sin lambda2)))
110.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify54.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	420	777
1	1833	599
2	5001	599

prune422.0ms

Filtered

99 candidates to 57 candidates (57.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 0.1b

Counts

111 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

4.0ms	(* (cos phi1) (sin phi2))
9.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))
5.0ms	(* (sin lambda2) (sin lambda1))
8.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos phi1) (sin phi2))
141.0ms	(* (sin phi1) (* (cos phi2) (* (sin lambda2) (sin lambda1))))
43.0ms	(* (sin lambda2) (sin lambda1))
111.0ms	(* (* (sin phi1) (cos phi2)) (* (cos lambda1) (cos lambda2)))

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	433	735
1	1823	572
2	5001	572

prune350.0ms

Filtered

96 candidates to 59 candidates (61.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	96	13	109

Merged error: 0.1b

Counts

109 → 13

regimes478.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	29
1	37	29

end0.0ms

sample8.6s

Algorithm

intervals

Results

6.3s	4568×	body	1280	valid
1.5s	1983×	body	640	valid
273.0ms	561×	body	320	valid
106.0ms	660×	body	80	valid
75.0ms	228×	body	160	valid

Details

sample270.0ms

simplify9.0ms

prune4.0ms

localize36.0ms

rewrite36.0ms

series180.0ms

simplify106.0ms

prune329.0ms

localize38.0ms

rewrite20.0ms

series292.0ms

simplify44.0ms

prune375.0ms

localize36.0ms

rewrite32.0ms

series297.0ms

simplify54.0ms

prune422.0ms

localize36.0ms

rewrite28.0ms

series340.0ms

simplify52.0ms

prune350.0ms

regimes478.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample8.6s

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