Details

analyze3.8s

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

sample292.0ms

Algorithm

intervals

Results

185.0ms	98×	body	1280	valid
48.0ms	45×	body	640	valid
17.0ms	25×	body	320	valid
16.0ms	77×	body	80	valid
5.0ms	11×	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

prune24.0ms

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

localize33.0ms

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)))))))

rewrite15.0ms

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:

4.0ms	(* (sin theta) (sin delta))
5.0ms	(* (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)))))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
34.0ms	(* (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))))
48.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify48.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4892	1209
1	4892	1209

prune167.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	60	9	69
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	62	9	71

Merged error: 0.1b

Counts

71 → 9

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
8×	`difference-of-squares`
7×	`pow1` `add-exp-log` `*-un-lft-identity` `add-cbrt-cube` `sqr-pow`
6×	`add-log-exp`
5×	`add-cube-cbrt`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
2×	`asin-acos` `pow-pow` `pow-exp` `rem-cube-cbrt`
1×	`difference-cubes` `cube-div` `cube-mult` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out--`

Counts

4 → 60

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)))))
9.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3))
5.0ms	(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)

series312.0ms

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)))))
237.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3))
65.0ms	(pow (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))) 3)

simplify40.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4963	1984
1	4963	1984

prune211.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	71	10	81

Merged error: 0.0b

Counts

81 → 10

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `add-exp-log` `unpow-prod-down` `pow-unpow` `cube-prod` `add-cbrt-cube` `add-log-exp`
3×	`cube-div`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `sin-cos-mult` `rem-cube-cbrt` `sqr-pow`
1×	`difference-cubes` `sub-neg` `asin-acos` `flip3--` `flip3-+` `diff-log` `associate-*r/` `pow-prod-down` `frac-add` `flip--` `flip-+`

Counts

4 → 69

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
11.0ms	(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)))
3.0ms	(pow (sin phi1) 3)
8.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)

series293.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
232.0ms	(- (pow (cos delta) 3) (* (pow (sin phi1) 3) (pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)))
5.0ms	(pow (sin phi1) 3)
50.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)

simplify33.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5446	1543

prune208.0ms

Filtered

51 candidates to 81 candidates (-58.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Merged error: 0.0b

Counts

91 → 10

localize59.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos delta) 6)
0.6b	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)
0.6b	(pow (sin phi1) 6)
0.9b	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 6)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down` `pow-unpow`
8×	`pow1` `add-exp-log`
5×	`add-cbrt-cube`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-log-exp` `sqr-pow`
3×	`cube-div` `cube-prod`
2×	`sin-cos-mult`
1×	`cube-mult` `flip3-+` `unpow3` `associate-*r/` `frac-add` `flip-+` `rem-cube-cbrt`

Counts

4 → 77

Calls

4 calls:

2.0ms	(pow (cos delta) 6)
10.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)
2.0ms	(pow (sin phi1) 6)
8.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 6)

series181.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(pow (cos delta) 6)
51.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 3)
7.0ms	(pow (sin phi1) 6)
117.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (sin delta) (cos theta)))) 6)

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5246	1226

prune186.0ms

Filtered

52 candidates to 89 candidates (-71.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	89	10	99

Merged error: 0.0b

Counts

99 → 10

regimes636.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	81	113
1	81	113

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.9s	3133×	body	1280	valid
2.0s	1817×	body	640	valid
508.0ms	714×	body	320	valid
436.0ms	2005×	body	80	valid
151.0ms	331×	body	160	valid

Details

analyze3.8s

sample292.0ms

simplify24.0ms

prune24.0ms

localize33.0ms

rewrite15.0ms

series97.0ms

simplify48.0ms

prune167.0ms

localize49.0ms

rewrite18.0ms

series312.0ms

simplify40.0ms

prune211.0ms

localize49.0ms

rewrite25.0ms

series293.0ms

simplify33.0ms

prune208.0ms

localize59.0ms

rewrite24.0ms

series181.0ms

simplify42.0ms

prune186.0ms

regimes636.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.4s

Profiling