Details

sample267.0ms

Algorithm

intervals

Results

164.0ms	104×	body	1280	valid
53.0ms	53×	body	640	valid
14.0ms	24×	body	320	valid
10.0ms	60×	body	80	valid
6.0ms	15×	body	160	valid

simplify7.0ms

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

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: 0.2b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (sin delta))
0.2b	(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))))))
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))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms	(* (sin phi1) (sin (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)))))))

series386.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin theta) (sin delta))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
155.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
180.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify103.0ms

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

prune101.0ms

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

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sqr-pow`
2×	`pow-to-exp` `unpow-prod-down` `unpow3` `*-commutative`
1×	`difference-cubes` `sub-neg` `flip3--` `flip--` `sin-mult` `difference-of-squares`

Counts

4 → 16

Calls

4 calls:

5.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
1.0ms	(pow (cos delta) 3)
5.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series1.1s

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
730.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
33.0ms	(pow (cos delta) 3)
230.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify50.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	371	502
1	1596	498
2	5001	497

prune260.0ms

Filtered

28 candidates to 22 candidates (78.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	5	28
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 0.1b

Counts

31 → 7

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`sqr-pow`
5×	`pow-to-exp` `unpow3`
2×	`associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `unswap-sqr`

Counts

4 → 17

Calls

4 calls:

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

series465.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(* (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3) (pow (sin phi1) 3))
33.0ms	(pow (cos delta) 3)
30.0ms	(pow (sin phi1) 3)
182.0ms	(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)

simplify81.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	185	285
1	632	285
2	2624	283
3	5001	283

prune287.0ms

Filtered

29 candidates to 23 candidates (79.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	27	9	36

Merged error: 0.1b

Counts

36 → 9

localize56.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (cos delta) 3)
0.4b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.6b	(pow (cos delta) 6)
0.7b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow-to-exp` `unpow-prod-down` `sqr-pow`
2×	`unpow3` `*-commutative`

Counts

4 → 14

Calls

4 calls:

2.0ms	(pow (cos delta) 3)
4.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
2.0ms	(pow (cos delta) 6)
4.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)

series733.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (cos delta) 3)
240.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
40.0ms	(pow (cos delta) 6)
425.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 6)

simplify89.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	201	278
1	676	278
2	2933	277
3	5001	277

prune404.0ms

Filtered

26 candidates to 20 candidates (76.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	23	3	26
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	24	11	35

Merged error: 0.1b

Counts

35 → 11

regimes593.0ms

Accuracy

0% (0.1b 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	62	76
1	64	76
2	64	76

end0.0ms

sample8.1s

Algorithm

intervals

Results

5.2s	3152×	body	1280	valid
1.7s	1850×	body	640	valid
453.0ms	714×	body	320	valid
349.0ms	1992×	body	80	valid
117.0ms	292×	body	160	valid