Details

analyze3.7s

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

sample314.0ms

Algorithm

intervals

Results

189.0ms	103×	body	1280	valid
66.0ms	65×	body	640	valid
25.0ms	29×	body	320	valid
11.0ms	53×	body	80	valid
3.0ms	6×	body	160	valid

simplify25.0ms

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: 0.2b

Counts

2 → 2

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin theta) (* (sin delta) (cos phi1)))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
38.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
43.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify49.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5126	1260

prune168.0ms

Filtered

51 candidates to 69 candidates (-35.3%)

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

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin delta) (* (cos phi1) (cos theta)))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

6.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
37.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
43.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4921	1258
1	4921	1258

prune139.0ms

Filtered

48 candidates to 69 candidates (-43.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Merged error: 0.1b

Counts

78 → 9

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.5b	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
7.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
34.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
145.0ms	(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))) (pow (sin phi1) 2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4947	1667
1	4947	1667

prune162.0ms

Filtered

45 candidates to 59 candidates (-31.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	58	10	68

Merged error: 0.1b

Counts

68 → 10

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.4b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
0.9b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

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

series129.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
34.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
46.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
43.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4871	1567
1	4871	1567

prune107.0ms

Filtered

50 candidates to 67 candidates (-34.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	66	11	77

Merged error: 0.1b

Counts

77 → 11

regimes640.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	33
1	56	33

end0.0ms

sample9.3s

Algorithm

intervals

Results

5.6s	3082×	body	1280	valid
2.2s	1859×	body	640	valid
534.0ms	711×	body	320	valid
408.0ms	2012×	body	80	valid
153.0ms	336×	body	160	valid

Details

analyze3.7s

sample314.0ms

simplify25.0ms

prune19.0ms

localize39.0ms

rewrite17.0ms

series103.0ms

simplify49.0ms

prune168.0ms

localize36.0ms

rewrite18.0ms

series101.0ms

simplify64.0ms

prune139.0ms

localize46.0ms

rewrite16.0ms

series189.0ms

simplify51.0ms

prune162.0ms

localize40.0ms

rewrite15.0ms

series129.0ms

simplify70.0ms

prune107.0ms

regimes640.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.3s

Profiling