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

sample299.0ms

Algorithm

intervals

Results

186.0ms	99×	body	1280	valid
61.0ms	60×	body	640	valid
13.0ms	67×	body	80	valid
12.0ms	17×	body	320	valid
6.0ms	13×	body	160	valid

simplify24.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune25.0ms

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

localize32.0ms

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))))
0.4b	(- (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)))))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin theta) (sin delta))
35.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
45.0ms	(- (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

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Merged error: 0.1b

Counts

71 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

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:

7.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
5.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
1.0ms	(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:

19.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
35.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))
6.0ms	(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))))))))

simplify47.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5126	1260

prune142.0ms

Filtered

51 candidates to 69 candidates (-35.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 0.1b

Counts

77 → 7

localize38.0ms

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	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
3.2b	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`log-prod`
11×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-exp-log`
9×	`pow1` `add-cube-cbrt` `add-cbrt-cube`
7×	`associate--r+`
6×	`unpow-prod-down`
5×	`add-log-exp`
3×	`asin-acos` `rem-log-exp` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`log-div` `sin-diff` `pow-sub` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `associate-r/` `associate-r` `pow-exp` `log-pow` `-commutative` `sin-cos-mult` `flip--` `distribute-lft-out--` `associate--r-` `difference-of-squares`

Counts

4 → 67

Calls

4 calls:

6.0ms	(* (sin theta) (* (sin delta) (cos phi1)))
1.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))
8.0ms	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
6.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

series135.0ms

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)))))
61.0ms	(- (cos delta) (log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta)))))))))
52.0ms	(log (pow (exp (sin phi1)) (sin (asin (+ (* (cos delta) (sin phi1)) (* (sin delta) (* (cos phi1) (cos theta))))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4831	1505
1	4831	1505

prune158.0ms

Filtered

61 candidates to 79 candidates (-29.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 0.1b

Counts

86 → 7

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))
0.3b	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
0.4b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
0.8b	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (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:

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

series129.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))))
5.0ms	(asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta)))))
43.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))
45.0ms	(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos phi1) (* (sin delta) (cos theta))))))))))

simplify66.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4871	1567
1	4871	1567

prune99.0ms

Filtered

48 candidates to 67 candidates (-39.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	65	9	74

Merged error: 0.0b

Counts

74 → 9

regimes607.0ms

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	58	35
1	58	35

end0.0ms

sample9.1s

Algorithm

intervals

Results

5.6s	3105×	body	1280	valid
2.1s	1841×	body	640	valid
474.0ms	678×	body	320	valid
418.0ms	2079×	body	80	valid
130.0ms	297×	body	160	valid

Details

analyze3.7s

sample299.0ms

simplify24.0ms

prune25.0ms

localize32.0ms

rewrite15.0ms

series95.0ms

simplify48.0ms

prune167.0ms

localize33.0ms

rewrite19.0ms

series103.0ms

simplify47.0ms

prune142.0ms

localize38.0ms

rewrite23.0ms

series135.0ms

simplify55.0ms

prune158.0ms

localize36.0ms

rewrite15.0ms

series129.0ms

simplify66.0ms

prune99.0ms

regimes607.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample9.1s

Profiling