Details

analyze3.6s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

sample371.0ms

Algorithm

intervals

Results

185.0ms	104×	body	1280	valid
58.0ms	60×	body	640	valid
17.0ms	27×	body	320	valid
11.0ms	60×	body	80	valid
2.0ms	5×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune19.0ms

Filtered

1 candidates to 1 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 → 2

localize37.0ms

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))))))
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 57

Calls

4 calls:

5.0ms	(* (sin theta) (sin delta))
8.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
37.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
44.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify50.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4892	1209
1	4892	1209

prune173.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	61	8	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Merged error: 0.0b

Counts

71 → 8

localize50.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.5b	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`asin-acos`
1×	`sqr-cos-a` `sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

4 → 36

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
7.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
143.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (pow (sin phi1) 2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4954	1401
1	4954	1401

prune147.0ms

Filtered

37 candidates to 48 candidates (-29.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	48	8	56

Merged error: 0.0b

Counts

56 → 8

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b	(acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.5b	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) (pow (sin phi1) 2))))
7.9b	(- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
2×	`acos-asin` `sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`sqr-cos-a` `asin-acos` `times-frac` `associate--l+` `distribute-lft-out--` `associate--r-`

Counts

4 → 43

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
1.0ms	(acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
8.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) (pow (sin phi1) 2))))
8.0ms	(- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
5.0ms	(acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
146.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))) (* (sin (- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) (pow (sin phi1) 2))))
10.0ms	(- (/ PI 2) (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

simplify34.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5083	1763

prune168.0ms

Filtered

43 candidates to 55 candidates (-27.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 0.0b

Counts

63 → 8

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos delta) 4)
13.1b	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
13.1b	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
13.1b	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`acos-asin` `cos-diff` `unpow-prod-down` `pow-unpow` `cos-acos`
1×	`pow-to-exp` `pow-pow` `pow-exp` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

2.0ms	(pow (cos delta) 4)
2.0ms	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
2.0ms	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
2.0ms	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(pow (cos delta) 4)
26.0ms	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
26.0ms	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))
29.0ms	(cos (acos (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4887	675
1	4887	675

prune128.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	56	8	64

Merged error: 0.0b

Counts

64 → 8

regimes554.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	118	155
1	118	155

end0.0ms

sample11.5s

Algorithm

intervals

Results

5.5s	3142×	body	1280	valid
1.9s	1829×	body	640	valid
447.0ms	687×	body	320	valid
373.0ms	2027×	body	80	valid
133.0ms	315×	body	160	valid

Details

analyze3.6s

sample371.0ms

simplify24.0ms

prune19.0ms

localize37.0ms

rewrite19.0ms

series96.0ms

simplify50.0ms

prune173.0ms

localize50.0ms

rewrite12.0ms

series158.0ms

simplify47.0ms

prune147.0ms

localize62.0ms

rewrite19.0ms

series167.0ms

simplify34.0ms

prune168.0ms

localize74.0ms

rewrite10.0ms

series86.0ms

simplify54.0ms

prune128.0ms

regimes554.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample11.5s

Profiling