Details

analyze932.0ms

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

sample67.0ms

Algorithm

intervals

Results

24.0ms	54×	body	1280	valid
12.0ms	121×	body	80	valid
11.0ms	41×	body	640	valid
6.0ms	28×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	10×	body	80	invalid

simplify437.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	382	11
1	382	11

prune11.0ms

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

localize23.0ms

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)))

rewrite26.0ms

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:

33.0ms	(- (/ 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)))

simplify49.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5054	989

prune177.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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:

12.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
4.0ms	(/ (* x 1.0) (tan B))
3.0ms	(/ 1.0 (sin B))

series66.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
22.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ 1.0 (sin B))

simplify43.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5045	732

prune103.0ms

Filtered

57 candidates to 73 candidates (-28.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 0.0b

Counts

84 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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:

22.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* 1.0 x))))
3.0ms	(/ 1.0 (sin B))
4.0ms	(/ (tan B) (* 1.0 x))
6.0ms	(/ 1 (/ (tan B) (* 1.0 x)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (/ 1.0 (sin B)) (/ 1 (/ (tan B) (* 1.0 x))))
4.0ms	(/ 1.0 (sin B))
13.0ms	(/ (tan B) (* 1.0 x))
19.0ms	(/ 1 (/ (tan B) (* 1.0 x)))

simplify55.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4942	1464
1	4942	1464

prune164.0ms

Filtered

94 candidates to 138 candidates (-46.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	139	8	147

Merged error: 0.0b

Counts

147 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

7.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* (cos B) (/ x (sin B)))))
3.0ms	(/ x (sin B))
3.0ms	(/ 1.0 (sin B))
7.0ms	(* (cos B) (/ x (sin B)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* (cos B) (/ x (sin B)))))
10.0ms	(/ x (sin B))
5.0ms	(/ 1.0 (sin B))
16.0ms	(* (cos B) (/ x (sin B)))

simplify60.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4976	1067
1	4976	1067

prune103.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	112	8	120

Merged error: 0.0b

Counts

120 → 8

regimes110.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	14
1	61	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

775.0ms	1766×	body	1280	valid
392.0ms	1404×	body	640	valid
267.0ms	3770×	body	80	valid
137.0ms	698×	body	320	valid
50.0ms	362×	body	160	valid
12.0ms	188×	body	80	invalid
0.0ms	2×	body	320	invalid
0.0ms	1×	body	640	invalid

Details

analyze932.0ms

sample67.0ms

simplify437.0ms

prune11.0ms

localize23.0ms

rewrite26.0ms

series81.0ms

simplify49.0ms

prune177.0ms

localize10.0ms

rewrite22.0ms

series66.0ms

simplify43.0ms

prune103.0ms

localize11.0ms

rewrite39.0ms

series66.0ms

simplify55.0ms

prune164.0ms

localize11.0ms

rewrite23.0ms

series57.0ms

simplify60.0ms

prune103.0ms

regimes110.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

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