Details

sample240.0ms

Algorithm

intervals

Results

190.0ms	114×	body	2560	valid
29.0ms	73×	body	1280	valid
7.0ms	42×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	21×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	4
1	11	4
2	11	4

prune2.0ms

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: 60.2b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (tan x))
2.4b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`frac-sub`
7×	`frac-2neg` `clear-num` `div-inv`
2×	`tan-quot` `prod-diff` `associate-/r/`
1×	`sub-neg` `flip3--` `fma-neg` `flip--` `distribute-lft-out--`

Counts

2 → 21

Calls

2 calls:

2.0ms	(/ 1.0 (tan x))
5.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

37.0ms	(/ 1.0 (tan x))
99.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify90.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	258	196
1	831	170
2	3396	155
3	5002	155

prune71.0ms

Filtered

27 candidates to 20 candidates (74.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	1	28

Merged error: 0.3b

Counts

28 → 1

localize16.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`fma-udef`

Counts

1 → 1

Calls

1 calls:

1.0ms

(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))

series116.0ms

Counts

1 → 3

Calls

1 calls:

116.0ms

(fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))

simplify112.0ms

Algorithm

egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	11
1	28	11
2	59	11
3	152	11
4	691	11
5	2386	11
6	5001	11

prune9.0ms

Filtered

4 candidates to 2 candidates (50.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	4	1	5

Merged error: 0.3b

Counts

5 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

1×	`associate-r` `*-commutative` `sqr-pow`

Counts

1 → 2

Calls

1 calls:

3.0ms

(* 0.0021164021164021165 (pow x 5))

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

(* 0.0021164021164021165 (pow x 5))

simplify89.0ms

Algorithm

egg-herbie

Counts

5 → 5

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	8
1	34	8
2	109	8
3	420	8
4	2251	8
5	5002	8

prune9.0ms

Filtered

5 candidates to 2 candidates (40.0%)

Pruning

1 alts after pruning (0 fresh and 1 done)

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

Merged error: 0.3b

Counts

6 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample7.0s

Algorithm

intervals

Results

5.2s	3318×	body	2560	valid
1.3s	2454×	body	1280	valid
196.0ms	1195×	body	640	valid
98.0ms	8000×	pre	80	true
66.0ms	653×	body	320	valid
25.0ms	337×	body	160	valid
2.0ms	43×	body	80	valid