Details

sample198.0ms

Algorithm

intervals

Results

134.0ms	101×	body	2560	valid
43.0ms	85×	body	1280	valid
6.0ms	37×	body	640	valid
3.0ms	256×	pre	80	true
2.0ms	19×	body	320	valid
1.0ms	13×	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: 59.9b

Counts

2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

3.5b	(- (/ 1.0 x) (/ 1.0 (tan x)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`frac-sub`
6×	`frac-2neg` `clear-num`
2×	`div-inv`
1×	`sub-neg` `flip3--` `flip--` `distribute-lft-out--`

Counts

1 → 14

Calls

1 calls:

5.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

series106.0ms

Counts

1 → 3

Calls

1 calls:

106.0ms

(- (/ 1.0 x) (/ 1.0 (tan x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	204	142
1	670	126
2	2489	111
3	5003	111

prune27.0ms

Filtered

17 candidates to 11 candidates (64.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	16	1	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	1	18

Merged error: 0.4b

Counts

18 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 10

Calls

3 calls:

8.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
2.0ms	(* 0.0021164021164021165 (pow x 5))
3.0ms	(* 0.022222222222222223 (pow x 3))

series150.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))
53.0ms	(* 0.0021164021164021165 (pow x 5))
37.0ms	(* 0.022222222222222223 (pow x 3))

simplify92.0ms

Algorithm

egg-herbie

Counts

19 → 19

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	101	97
1	358	96
2	1892	96
3	5001	96

prune36.0ms

Filtered

19 candidates to 10 candidates (52.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	16	3	19
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	17	3	20

Merged error: 0.4b

Counts

20 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 13

Calls

4 calls:

12.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
5.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
3.0ms	(* 0.0021164021164021165 (pow x 5))
3.0ms	(* 0.022222222222222223 (pow x 3))

series301.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+ (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x))
140.0ms	(+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))
56.0ms	(* 0.0021164021164021165 (pow x 5))
38.0ms	(* 0.022222222222222223 (pow x 3))

simplify124.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 2 (19.0ms)

Iter	Nodes	Cost
0	142	151
1	511	148
2	2515	142
3	5001	142

prune49.0ms

Filtered

25 candidates to 13 candidates (52.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	24	1	25
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Merged error: 0.4b

Counts

28 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.022222222222222223 (pow x 3))
0.1b	(* 0.022222222222222223 (pow x 3))
0.3b	(* (* 0.3333333333333333 x) (* 0.3333333333333333 x))
29.8b	(/ (- (* (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))) (* (* 0.3333333333333333 x) (* 0.3333333333333333 x))) (- (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-commutative`
6×	`associate-r`
4×	`associate-/l*` `difference-of-squares`
2×	`flip3--` `unpow3` `swap-sqr` `associate-l` `associate-/r/` `flip--` `associate-/l/` `sqr-pow`
1×	`pow2` `frac-2neg` `div-sub` `clear-num` `div-inv`

Counts

4 → 26

Calls

4 calls:

3.0ms	(* 0.022222222222222223 (pow x 3))
3.0ms	(* 0.022222222222222223 (pow x 3))
8.0ms	(* (* 0.3333333333333333 x) (* 0.3333333333333333 x))
24.0ms	(/ (- (* (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))) (* (* 0.3333333333333333 x) (* 0.3333333333333333 x))) (- (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 0.022222222222222223 (pow x 3))
43.0ms	(* 0.022222222222222223 (pow x 3))
25.0ms	(* (* 0.3333333333333333 x) (* 0.3333333333333333 x))
183.0ms	(/ (- (* (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5)))) (* (* 0.3333333333333333 x) (* 0.3333333333333333 x))) (- (+ (* 0.022222222222222223 (pow x 3)) (* 0.0021164021164021165 (pow x 5))) (* 0.3333333333333333 x)))

simplify31.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	170	234
1	774	234
2	5001	219

prune91.0ms

Filtered

38 candidates to 25 candidates (65.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	34	4	38
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	36	5	41

Merged error: 0.2b

Counts

41 → 5

regimes23.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	7
1	18	7

end0.0ms

sample6.9s

Algorithm

intervals

Results

5.0s	3167×	body	2560	valid
1.3s	2572×	body	1280	valid
210.0ms	1255×	body	640	valid
105.0ms	8000×	pre	80	true
63.0ms	642×	body	320	valid
23.0ms	322×	body	160	valid
2.0ms	42×	body	80	valid