Details

sample255.0ms

Algorithm

intervals

Results

153.0ms	95×	body	1280	valid
60.0ms	68×	body	640	valid
11.0ms	68×	body	80	valid
9.0ms	16×	body	320	valid
3.0ms	9×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	22
1	61	22
2	71	22
3	72	22
4	72	22

prune5.0ms

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

localize38.0ms

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)))))))

rewrite13.0ms

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)))))))

series384.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (sin theta) (sin delta))
151.0ms	(* (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))))
177.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify111.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 4 (108.0ms)

Iter	Nodes	Cost
0	178	258
1	410	254
2	1230	249
3	3437	249
4	5001	247

prune102.0ms

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

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite13.0ms

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))
5.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin theta) (sin delta))
155.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
179.0ms	(- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify109.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 4 (105.0ms)

Iter	Nodes	Cost
0	179	258
1	408	254
2	1225	249
3	3423	249
4	5001	247

prune98.0ms

Filtered

21 candidates to 13 candidates (61.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	21	3	24

Merged error: 0.1b

Counts

24 → 3

localize44.0ms

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))))
0.4b	(pow (cos delta) 3)
0.4b	(pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

2×	`pow-to-exp` `unpow-prod-down` `asin-acos` `unpow3` `sqr-pow`
1×	`*-commutative`

Counts

4 → 10

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(pow (cos delta) 3)
5.0ms	(pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)

series279.0ms

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))))
29.0ms	(pow (cos delta) 3)
236.0ms	(pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)

simplify63.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	140	235
1	438	233
2	1692	233
3	5002	233

prune159.0ms

Filtered

22 candidates to 15 candidates (68.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	1	1
Picked	1	0	1
Done	1	0	1
Total	22	3	25

Merged error: 0.1b

Counts

25 → 3

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(pow (cos delta) 3)
0.4b	(pow (sin phi1) 3)
0.6b	(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

3×	`pow-to-exp` `unpow3` `sqr-pow`
1×	`asin-acos`

Counts

4 → 10

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(pow (cos delta) 3)
2.0ms	(pow (sin phi1) 3)
3.0ms	(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

series244.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
28.0ms	(pow (cos delta) 3)
30.0ms	(pow (sin phi1) 3)
179.0ms	(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

simplify51.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	146	170
1	404	166
2	1438	165
3	5001	165

prune148.0ms

Filtered

22 candidates to 15 candidates (68.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	22	3	25

Merged error: 0.1b

Counts

25 → 3

regimes180.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	57
1	40	57

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.0s	3130×	body	1280	valid
1.7s	1828×	body	640	valid
422.0ms	684×	body	320	valid
337.0ms	2049×	body	80	valid
117.0ms	309×	body	160	valid