Details

sample493.0ms

Algorithm

intervals

Results

147.0ms	52×	body	2560	valid
61.0ms	89×	body	1280	valid
15.0ms	62×	body	640	valid
4.0ms	25×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	11×	body	80	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	17	5
2	19	5
3	19	5

prune4.0ms

Filtered

1 candidates to 0 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: 32.8b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x (sin x)) (- x (tan x)))
1.9b	(- x (tan x))
1.9b	(- x (sin x))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`flip3--` `flip--`
2×	`sub-neg` `associate-/r/` `associate-/l/`
1×	`frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

3 → 16

Calls

3 calls:

4.0ms	(/ (- x (sin x)) (- x (tan x)))
2.0ms	(- x (tan x))
5.0ms	(- x (sin x))

series189.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (- x (sin x)) (- x (tan x)))
51.0ms	(- x (tan x))
57.0ms	(- x (sin x))

simplify65.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	219	172
1	719	167
2	2394	167
3	5001	167

prune82.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	4	26

Merged error: 0.0b

Counts

26 → 4

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(fma 27/2800 (pow x 4) 1/2)
15.8b	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`fma-udef`

Counts

2 → 2

Calls

2 calls:

1.0ms	(fma 27/2800 (pow x 4) 1/2)
1.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

series129.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(fma 27/2800 (pow x 4) 1/2)
45.0ms	(fma 9/40 (pow x 2) (- (fma 27/2800 (pow x 4) 1/2)))

simplify200.0ms

Algorithm

egg-herbie

Counts

8 → 8

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	25
1	87	25
2	245	25
3	799	25
4	4079	25
5	5001	25

prune20.0ms

Filtered

8 candidates to 2 candidates (25.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	8	0	8
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	8	4	12

Merged error: 0.0b

Counts

12 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (- x (tan x)))
1.8b	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

20×	`associate-/r/`
13×	`flip3--` `flip--`
10×	`div-inv`
9×	`frac-2neg` `prod-diff` `frac-sub`
7×	`clear-num`
3×	`sub-neg` `distribute-rgt-out--` `fma-neg`
2×	`sub-div`

Counts

4 → 43

Calls

4 calls:

4.0ms	(/ (sin x) (- x (tan x)))
8.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
2.0ms	(- x (tan x))
2.0ms	(- x (tan x))

series345.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/ (sin x) (- x (tan x)))
179.0ms	(- (/ x (- x (tan x))) (/ (sin x) (- x (tan x))))
49.0ms	(- x (tan x))
55.0ms	(- x (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	409	822
1	1493	708
2	5001	637

prune128.0ms

Filtered

55 candidates to 39 candidates (70.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	55	4	59

Merged error: 0.0b

Counts

59 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

1.9b	(- x (tan x))
1.9b	(- x (tan x))
1.9b	(- x (tan x))
1.9b	(- x (tan x))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

4×	`sub-neg` `flip3--` `flip--`

Counts

4 → 16

Calls

4 calls:

2.0ms	(- x (tan x))
2.0ms	(- x (tan x))
3.0ms	(- x (tan x))
2.0ms	(- x (tan x))

series210.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(- x (tan x))
49.0ms	(- x (tan x))
55.0ms	(- x (tan x))
50.0ms	(- x (tan x))

simplify135.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	75	152
1	170	144
2	428	144
3	1134	144
4	4140	144
5	5001	144

prune76.0ms

Filtered

28 candidates to 20 candidates (71.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	28	4	32

Merged error: 0.0b

Counts

32 → 4

regimes35.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.8b

bsearch68.0ms

Steps

Iters	Range		Point
9	2.5653698016906928e-06	357.20278190505735	0.02550642089016014
7	-0.6319501064166059	-0.005814372128176944	-0.027158292991570857

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	29
1	35	29
2	37	29
3	37	29

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.6s	1573×	body	2560	valid
1.6s	2832×	body	1280	valid
469.0ms	1870×	body	640	valid
146.0ms	926×	body	320	valid
59.0ms	471×	body	160	valid
22.0ms	328×	body	80	valid