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

sample474.0ms

Algorithm

intervals

Results

350.0ms	99×	body	1280	valid
71.0ms	63×	body	640	valid
15.0ms	21×	body	320	valid
13.0ms	64×	body	80	valid
4.0ms	9×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	44	33
1	44	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:

0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
0.3b	(* (sin delta) (* (cos phi1) (cos theta)))
0.3b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.5b	(- (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:

1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
7.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
6.0ms	(* (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:

6.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
16.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
37.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
44.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4948	1258
1	4948	1258

prune129.0ms

Filtered

48 candidates to 69 candidates (-43.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 0.1b

Counts

71 → 5

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin delta) (* (cos phi1) (cos theta)))
0.3b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
0.8b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 66

Calls

4 calls:

7.0ms	(* (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))))))))
3.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))))

series141.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (sin delta) (* (cos phi1) (cos theta)))
36.0ms	(* (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))))))))
46.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4936	1562
1	4936	1562

prune135.0ms

Filtered

54 candidates to 78 candidates (-44.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0.1b

Counts

83 → 5

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
0.5b	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3))
0.5b	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
4×	`cube-div`
3×	`pow-unpow` `flip3--` `associate-r` `associate-l` `flip--`
2×	`cube-mult` `cbrt-div` `unpow3` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `pow-pow` `pow1/3` `diff-log` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `sin-mult` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

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

series206.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (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	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3))
81.0ms	(pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 3)

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4945	2545
1	4945	2545

prune145.0ms

Filtered

55 candidates to 90 candidates (-63.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	90	5	95

Merged error: 0.1b

Counts

95 → 5

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

11×	`cbrt-prod`
8×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`unpow-prod-down` `flip3--` `flip--`
2×	`sub-neg` `cbrt-div` `pow1/3` `diff-log`
1×	`unpow2` `sqr-pow`

Counts

4 → 51

Calls

4 calls:

4.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
2.0ms	(cbrt (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
4.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 2))

series297.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
44.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))
89.0ms	(cbrt (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
119.0ms	(cbrt (pow (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))) 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4878	1904
1	4878	1904

prune103.0ms

Filtered

48 candidates to 63 candidates (-31.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	62	6	68

Merged error: 0.1b

Counts

68 → 6

regimes462.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	35
1	32	35

end0.0ms

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

sample9.2s

Algorithm

intervals

Results

5.7s	3115×	body	1280	valid
2.0s	1828×	body	640	valid
520.0ms	731×	body	320	valid
426.0ms	2009×	body	80	valid
161.0ms	317×	body	160	valid

Details

analyze3.8s

sample474.0ms

simplify4.0ms

prune24.0ms

localize33.0ms

rewrite18.0ms

series103.0ms

simplify70.0ms

prune129.0ms

localize37.0ms

rewrite20.0ms

series141.0ms

simplify73.0ms

prune135.0ms

localize37.0ms

rewrite18.0ms

series206.0ms

simplify54.0ms

prune145.0ms

localize40.0ms

rewrite14.0ms

series297.0ms

simplify65.0ms

prune103.0ms

regimes462.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze3.8s

sample9.2s

Profiling