Details

sample274.0ms

Algorithm

intervals

Results

175.0ms	104×	body	1280	valid
48.0ms	53×	body	640	valid
15.0ms	24×	body	320	valid
10.0ms	60×	body	80	valid
6.0ms	15×	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: 0.2b

Counts

2 → 1

localize39.0ms

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)))))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* (sin theta) (sin delta))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
145.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
175.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 4 (102.0ms)

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

prune98.0ms

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: 0.2b

Counts

22 → 3

localize43.0ms

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)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 26

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

series1.3s

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
926.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
28.0ms	(pow (cos delta) 3)
230.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify62.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	437	1156
1	1900	872
2	5001	870

prune299.0ms

Filtered

38 candidates to 26 candidates (68.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	31	7	38
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	33	8	41

Merged error: 0.1b

Counts

41 → 8

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 17

Calls

4 calls:

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

series737.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
227.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
234.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
39.0ms	(pow (cos delta) 6)

simplify56.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	134	416
1	412	412
2	1650	412
3	5001	412

prune329.0ms

Filtered

29 candidates to 24 candidates (82.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	28	1	29
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	30	7	37

Merged error: 0.1b

Counts

37 → 7

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 15

Calls

4 calls:

4.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
4.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
3.0ms	(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
2.0ms	(pow (cos delta) 6)

series683.0ms

Counts

4 → 12

Calls

4 calls:

230.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
234.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
179.0ms	(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
39.0ms	(pow (cos delta) 6)

simplify74.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	163	371
1	534	365
2	2231	365
3	5002	365

prune260.0ms

Filtered

27 candidates to 22 candidates (81.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	28	6	34

Merged error: 0.1b

Counts

34 → 6

regimes389.0ms

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	52	87
1	52	87

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.0s	3152×	body	1280	valid
1.7s	1850×	body	640	valid
423.0ms	714×	body	320	valid
330.0ms	1992×	body	80	valid
114.0ms	292×	body	160	valid