Details

sample253.0ms

Algorithm

intervals

Results

146.0ms	95×	body	1280	valid
64.0ms	68×	body	640	valid
11.0ms	68×	body	80	valid
9.0ms	16×	body	320	valid
3.0ms	9×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	22
1	56	22
2	59	22
3	59	22

prune6.0ms

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: 0.1b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.3b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

2×	`*-commutative` `sin-mult`
1×	`sub-neg` `asin-acos` `flip3--` `flip--`

Counts

4 → 9

Calls

4 calls:

3.0ms	(* (sin theta) (sin delta))
4.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series382.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin theta) (sin delta))
153.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
178.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify101.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	170	260
1	363	259
2	1071	257
3	2991	257
4	5002	257

prune97.0ms

Filtered

21 candidates to 13 candidates (61.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	18	3	21
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	3	22

Merged error: 0.1b

Counts

22 → 3

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.3b	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

10×	`sin-mult`
9×	`*-commutative`
5×	`cos-mult`
4×	`difference-of-squares`
3×	`associate-r/` `associate-l/` `frac-sub`
2×	`frac-times` `asin-acos` `swap-sqr` `associate-r` `associate-l` `sub-div`
1×	`pow2` `sub-neg` `sqr-cos` `flip3--` `associate--l+` `flip--`

Counts

4 → 27

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
13.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series681.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
179.0ms	(* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
488.0ms	(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	330	1089
1	1395	1046
2	5001	1014

prune240.0ms

Filtered

39 candidates to 25 candidates (64.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	35	4	39
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	38	4	42

Merged error: 0.1b

Counts

42 → 4

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(pow (sin phi1) 3)
0.4b	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))
0.4b	(pow (sin phi1) 4)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqr-pow`
6×	`unpow2`
4×	`difference-of-squares` `unswap-sqr`
2×	`pow-to-exp` `distribute-rgt-out--` `associate-r`
1×	`sub-neg` `asin-acos` `flip3--` `unpow3` `flip--`

Counts

4 → 16

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(pow (sin phi1) 3)
6.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))
2.0ms	(pow (sin phi1) 4)

series164.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
30.0ms	(pow (sin phi1) 3)
94.0ms	(- (pow (cos delta) 2) (* (pow (sin phi1) 4) (pow (cos delta) 2)))
32.0ms	(pow (sin phi1) 4)

simplify133.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	207	213
1	619	200
2	2741	195
3	5002	195

prune234.0ms

Filtered

28 candidates to 17 candidates (60.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Merged error: 0.1b

Counts

32 → 4

localize72.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos delta) 4)
0.4b	(pow (sin phi1) 4)
0.4b	(pow (sin phi1) 4)
0.7b	(pow (sin phi1) 8)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow-to-exp` `sqr-pow`

Counts

4 → 8

Calls

4 calls:

1.0ms	(pow (cos delta) 4)
2.0ms	(pow (sin phi1) 4)
2.0ms	(pow (sin phi1) 4)
2.0ms	(pow (sin phi1) 8)

series144.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(pow (cos delta) 4)
31.0ms	(pow (sin phi1) 4)
30.0ms	(pow (sin phi1) 4)
49.0ms	(pow (sin phi1) 8)

simplify43.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	71
1	319	71
2	1017	71
3	5001	71

prune194.0ms

Filtered

20 candidates to 12 candidates (60.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	1	20
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	20	4	24

Merged error: 0.1b

Counts

24 → 4

regimes283.0ms

Accuracy

0% (0.0b 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	63	54
1	63	54

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.0s	3130×	body	1280	valid
1.6s	1828×	body	640	valid
410.0ms	684×	body	320	valid
337.0ms	2049×	body	80	valid
119.0ms	309×	body	160	valid