Details

analyze886.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
18.7%	81.2%	0.1%	7
25%	73.4%	1.7%	8
28.1%	68.7%	3.2%	9
31.2%	62.8%	6%	10
32.8%	60.1%	7.1%	11
34.3%	56.7%	9%	12
35.1%	55.2%	9.7%	13
35.9%	53.4%	10.7%	14

sample71.0ms

Algorithm

intervals

Results

26.0ms	60×	body	1280	valid
15.0ms	54×	body	640	valid
12.0ms	115×	body	80	valid
3.0ms	15×	body	320	valid
2.0ms	12×	body	160	valid
0.0ms	7×	body	80	invalid

simplify441.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	854	11
1	854	11

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.2b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 100

Calls

4 calls:

6.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))

series81.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1.0 (tan B))
33.0ms	(* x (/ 1.0 (tan B)))

simplify63.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4968	987
1	4968	987

prune201.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	9	113

Merged error: 0.0b

Counts

113 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (* x 1.0) (tan B))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `times-frac`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `div-exp`
2×	`frac-2neg` `clear-num` `div-inv` `difference-of-squares`
1×	`tan-quot` `sub-neg` `flip3--` `diff-log` `prod-exp` `associate-/r/` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 64

Calls

3 calls:

10.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
3.0ms	(/ 1.0 (sin B))
5.0ms	(/ (* x 1.0) (tan B))

series56.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ 1.0 (sin B))
23.0ms	(/ (* x 1.0) (tan B))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4963	728
1	4963	728

prune119.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Merged error: 0.0b

Counts

82 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ (tan B) (* x 1.0))
0.3b	(/ 1 (/ (tan B) (* x 1.0)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
47×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`add-cube-cbrt`
20×	`add-cbrt-cube`
15×	`div-exp`
11×	`associate-/r*`
9×	`associate-/l*`
8×	`cbrt-undiv` `div-inv`
6×	`add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`prod-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `distribute-lft-out--`
2×	`cbrt-unprod`
1×	`tan-quot` `sub-neg` `flip3--` `pow-flip` `diff-log` `associate-/r/` `frac-sub` `flip--` `associate-/l/` `inv-pow`

Counts

4 → 126

Calls

4 calls:

20.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ (tan B) (* x 1.0))
6.0ms	(/ 1 (/ (tan B) (* x 1.0)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* x 1.0))))
4.0ms	(/ 1.0 (sin B))
13.0ms	(/ (tan B) (* x 1.0))
19.0ms	(/ 1 (/ (tan B) (* x 1.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4915	1460
1	4915	1460

prune183.0ms

Filtered

93 candidates to 138 candidates (-48.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	139	8	147

Merged error: 0.0b

Counts

147 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))
0.5b	(cbrt (/ 1.0 (tan B)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

110×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
17×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`tan-quot` `cbrt-div` `associate-/r/` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 150

Calls

4 calls:

14.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
3.0ms	(cbrt (/ 1.0 (tan B)))
3.0ms	(cbrt (/ 1.0 (tan B)))
3.0ms	(cbrt (/ 1.0 (tan B)))

series154.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cbrt (/ 1.0 (tan B))) (cbrt (/ 1.0 (tan B))))
35.0ms	(cbrt (/ 1.0 (tan B)))
32.0ms	(cbrt (/ 1.0 (tan B)))
38.0ms	(cbrt (/ 1.0 (tan B)))

simplify70.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4910	1987
1	4910	1987

prune363.0ms

Filtered

133 candidates to 162 candidates (-21.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	162	8	170

Merged error: 0.0b

Counts

170 → 8

regimes123.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	11
1	80	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

756.0ms	1718×	body	1280	valid
401.0ms	1436×	body	640	valid
269.0ms	3768×	body	80	valid
127.0ms	660×	body	320	valid
60.0ms	418×	body	160	valid
11.0ms	160×	body	80	invalid
1.0ms	2×	body	1280	invalid

Details

analyze886.0ms

sample71.0ms

simplify441.0ms

prune12.0ms

localize22.0ms

rewrite28.0ms

series81.0ms

simplify63.0ms

prune201.0ms

localize10.0ms

rewrite20.0ms

series56.0ms

simplify46.0ms

prune119.0ms

localize11.0ms

rewrite40.0ms

series63.0ms

simplify68.0ms

prune183.0ms

localize16.0ms

rewrite29.0ms

series154.0ms

simplify70.0ms

prune363.0ms

regimes123.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

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