Details

analyze918.0ms

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

sample65.0ms

Algorithm

intervals

Results

29.0ms	66×	body	1280	valid
11.0ms	38×	body	640	valid
9.0ms	124×	body	80	valid
4.0ms	22×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	1×	body	80	invalid

simplify453.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

localize13.0ms

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))
0.1b	(/ 1.0 (tan B))
0.2b	(* 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))
3.0ms	(/ 1.0 (tan B))
9.0ms	(* x (/ 1.0 (tan B)))

series90.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
5.0ms	(/ 1.0 (sin B))
11.0ms	(/ 1.0 (tan B))
47.0ms	(* x (/ 1.0 (tan B)))

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5054	989

prune159.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	106	6	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	6	113

Merged error: 0b

Counts

113 → 6

localize13.0ms

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))

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

series54.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
23.0ms	(/ (* x 1.0) (tan B))
5.0ms	(/ 1.0 (sin B))

simplify45.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5045	732

prune93.0ms

Filtered

57 candidates to 73 candidates (-28.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Merged error: 0b

Counts

79 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

9.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* (cos B) (/ x (sin B)))))
3.0ms	(/ 1.0 (sin B))
3.0ms	(/ x (sin B))
7.0ms	(* (cos B) (/ x (sin B)))

series55.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (/ 1.0 (sin B)) (* 1.0 (* (cos B) (/ x (sin B)))))
4.0ms	(/ 1.0 (sin B))
11.0ms	(/ x (sin B))
15.0ms	(* (cos B) (/ x (sin B)))

simplify61.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4976	1067
1	4976	1067

prune120.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	112	6	118

Merged error: 0b

Counts

118 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.7b	(cbrt x)
0.7b	(cbrt x)
0.7b	(cbrt x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series95.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt x) (cbrt x))
24.0ms	(cbrt x)
22.0ms	(cbrt x)
24.0ms	(cbrt x)

simplify47.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5165	356

prune76.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	85	6	91

Merged error: 0b

Counts

91 → 6

regimes97.0ms

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	43	11
1	43	11

end0.0ms

sample1.8s

Algorithm

intervals

Results

785.0ms	1757×	body	1280	valid
395.0ms	1442×	body	640	valid
260.0ms	3730×	body	80	valid
145.0ms	726×	body	320	valid
48.0ms	345×	body	160	valid
11.0ms	163×	body	80	invalid
0.0ms	1×	body	1280	invalid
0.0ms	1×	body	640	invalid

Details

analyze918.0ms

sample65.0ms

simplify453.0ms

prune11.0ms

localize13.0ms

rewrite26.0ms

series90.0ms

simplify47.0ms

prune159.0ms

localize13.0ms

rewrite20.0ms

series54.0ms

simplify45.0ms

prune93.0ms

localize12.0ms

rewrite25.0ms

series55.0ms

simplify61.0ms

prune120.0ms

localize15.0ms

rewrite11.0ms

series95.0ms

simplify47.0ms

prune76.0ms

regimes97.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.8s

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