Details

sample240.0ms

Algorithm

intervals

Results

190.0ms	114×	body	2560	valid
27.0ms	73×	body	1280	valid
7.0ms	42×	body	640	valid
4.0ms	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

localize6.0ms

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`
3×	`div-inv`
1×	`tan-quot` `sub-neg` `flip3--` `associate-/r/` `flip--` `distribute-lft-out--`

Counts

2 → 18

Calls

2 calls:

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

series150.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(/ 1.0 (tan x))
110.0ms	(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	215	166
1	698	150
2	2607	135
3	5003	135

prune43.0ms

Filtered

24 candidates to 17 candidates (70.8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	1	25

Merged error: 0.3b

Counts

25 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

3×	`associate-r`
2×	`*-commutative` `sqr-pow`
1×	`+-commutative` `flip3-+` `unpow3` `flip-+`

Counts

3 → 8

Calls

3 calls:

4.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
2.0ms	(* 0.0021164021164021165 (pow x 5))
3.0ms	(* 0.022222222222222223 (pow x 3))

series232.0ms

Counts

3 → 9

Calls

3 calls:

139.0ms	(+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))
54.0ms	(* 0.0021164021164021165 (pow x 5))
38.0ms	(* 0.022222222222222223 (pow x 3))

simplify45.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	86	61
1	269	60
2	1011	59
3	5001	59

prune30.0ms

Filtered

17 candidates to 8 candidates (47.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	15	3	18

Merged error: 0.3b

Counts

18 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
0.2b	(* (* 0.3333333333333333 x) (* 0.3333333333333333 x))
29.6b	(/ (+ (- (* (* 0.3333333333333333 x) (* 0.3333333333333333 x))) (* 0.0021164021164021165 (* 0.0021164021164021165 (pow x 10)))) (- (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

7×	`*-commutative`
5×	`associate-r`
2×	`swap-sqr` `associate-l` `associate-/r/` `associate-/l/` `sqr-pow`
1×	`pow2` `neg-sub0` `associate-+l-` `flip3--` `frac-2neg` `flip3-+` `unpow3` `div-sub` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 21

Calls

4 calls:

3.0ms	(* 0.0021164021164021165 (pow x 5))
3.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(* (* 0.3333333333333333 x) (* 0.3333333333333333 x))
16.0ms	(/ (+ (- (* (* 0.3333333333333333 x) (* 0.3333333333333333 x))) (* 0.0021164021164021165 (* 0.0021164021164021165 (pow x 10)))) (- (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 0.0021164021164021165 (pow x 5))
42.0ms	(* 0.022222222222222223 (pow x 3))
25.0ms	(* (* 0.3333333333333333 x) (* 0.3333333333333333 x))
260.0ms	(/ (+ (- (* (* 0.3333333333333333 x) (* 0.3333333333333333 x))) (* 0.0021164021164021165 (* 0.0021164021164021165 (pow x 10)))) (- (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

simplify38.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	185	174
1	787	154
2	5001	146

prune136.0ms

Filtered

33 candidates to 23 candidates (69.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	27	6	33
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	28	8	36

Merged error: 0.2b

Counts

36 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.0021164021164021165 (pow x 5))
0.1b	(* 0.022222222222222223 (pow x 3))
0.3b	(/ 1 (+ (* 0.3333333333333333 x) (* 0.0021164021164021165 (pow x 5))))
0.3b	(/ 1 (/ 1 (+ (* 0.3333333333333333 x) (* 0.0021164021164021165 (pow x 5)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

7×	`associate-/r/`
4×	`clear-num`
3×	`frac-2neg` `associate-r` `associate-/r*` `div-inv` `inv-pow`
2×	`flip3-+` `*-commutative` `flip-+` `remove-double-div` `sqr-pow`
1×	`pow-flip` `unpow3`

Counts

4 → 24

Calls

4 calls:

3.0ms	(* 0.0021164021164021165 (pow x 5))
3.0ms	(* 0.022222222222222223 (pow x 3))
5.0ms	(/ 1 (+ (* 0.3333333333333333 x) (* 0.0021164021164021165 (pow x 5))))
6.0ms	(/ 1 (/ 1 (+ (* 0.3333333333333333 x) (* 0.0021164021164021165 (pow x 5)))))

series375.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(* 0.0021164021164021165 (pow x 5))
41.0ms	(* 0.022222222222222223 (pow x 3))
138.0ms	(/ 1 (+ (* 0.3333333333333333 x) (* 0.0021164021164021165 (pow x 5))))
147.0ms	(/ 1 (/ 1 (+ (* 0.3333333333333333 x) (* 0.0021164021164021165 (pow x 5)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	154	126
1	467	125
2	1727	122
3	5002	118

prune73.0ms

Filtered

36 candidates to 22 candidates (61.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	35	1	36
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	38	6	44

Merged error: 0.1b

Counts

44 → 6

regimes33.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	11
1	25	11

end0.0ms

sample7.0s

Algorithm

intervals

Results

5.2s	3318×	body	2560	valid
1.3s	2454×	body	1280	valid
201.0ms	1195×	body	640	valid
105.0ms	8000×	pre	80	true
68.0ms	653×	body	320	valid
28.0ms	337×	body	160	valid
2.0ms	43×	body	80	valid