Details

analyze715.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample43.0ms

Algorithm

intervals

Results

12.0ms	44×	body	1280	valid
10.0ms	137×	body	80	valid
8.0ms	45×	body	640	valid
2.0ms	16×	body	320	valid
1.0ms	14×	body	160	valid

simplify541.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5284	15

prune4.0ms

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: 0.3b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
0.1b	(- 1.0 (* (tan x) (tan x)))
0.3b	(* (tan x) (tan x))
0.3b	(* (tan x) (tan x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
12×	`times-frac`
10×	`add-exp-log` `add-cbrt-cube`
8×	`tan-quot`
6×	`swap-sqr` `associate-r` `associate-l` `add-log-exp`
5×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*`
2×	`pow2` `frac-times` `flip3--` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

6.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
3.0ms	(- 1.0 (* (tan x) (tan x)))
5.0ms	(* (tan x) (tan x))
7.0ms	(* (tan x) (tan x))

series76.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
9.0ms	(* (tan x) (tan x))
26.0ms	(* (tan x) (tan x))

simplify54.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune220.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	104	12	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	12	117

Merged error: 0.1b

Counts

117 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (pow (tan x) 2))
0.1b	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

242×	`times-frac`
201×	`add-sqr-sqrt`
197×	`*-un-lft-identity`
99×	`add-cube-cbrt`
68×	`difference-of-squares`
38×	`associate-/r*`
32×	`distribute-lft-out`
23×	`unpow-prod-down`
19×	`unpow2` `sqr-pow`
17×	`add-exp-log` `distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
7×	`pow1` `div-exp`
6×	`pow-unpow` `add-log-exp`
5×	`flip3--` `flip--` `div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`pow-to-exp` `rec-exp` `pow-pow` `1-exp` `pow-exp`
1×	`sub-neg` `pow-flip` `frac-2neg` `diff-log` `clear-num` `inv-pow`

Counts

4 → 228

Calls

4 calls:

5.0ms	(- 1.0 (pow (tan x) 2))
18.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series62.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- 1.0 (pow (tan x) 2))
35.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
9.0ms	(pow (tan x) 2)
9.0ms	(pow (tan x) 2)

simplify89.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4972	4413
1	4972	4413

prune341.0ms

Filtered

115 candidates to 240 candidates (-108.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	236	4	240
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	238	14	252

Merged error: 0.0b

Counts

252 → 14

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)
0.4b	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
25×	`times-frac`
12×	`add-cube-cbrt`
11×	`unpow-prod-down`
10×	`difference-of-squares`
9×	`pow-unpow`
7×	`pow1` `add-exp-log` `distribute-lft-out--`
6×	`add-log-exp`
5×	`unpow2` `sqr-pow`
4×	`associate-/r/` `add-cbrt-cube` `distribute-lft-out`
3×	`pow-to-exp` `distribute-rgt-out--` `pow-pow` `pow-exp`
2×	`flip3-+` `flip-+` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `sub-div`

Counts

4 → 87

Calls

4 calls:

3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)
49.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow (tan x) 2)
9.0ms	(pow (tan x) 2)
11.0ms	(pow (tan x) 2)
52.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

simplify33.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5194	1408

prune206.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	95	4	99
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 0.0b

Counts

113 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (- 1.0 (pow (tan x) 2)))
0.2b	(/ (/ 1 (+ (pow (tan x) 2) 1.0)) (/ 1 (- 1.0 (pow (tan x) 2))))
0.3b	(pow (tan x) 2)
0.3b	(pow (tan x) 2)

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

1392×	`times-frac`
863×	`add-sqr-sqrt`
805×	`*-un-lft-identity`
497×	`add-cube-cbrt`
244×	`difference-of-squares`
103×	`associate-/r/`
93×	`distribute-lft-out`
67×	`unpow-prod-down`
63×	`unpow2` `sqr-pow`
61×	`distribute-lft-out--`
52×	`div-inv`
50×	`add-exp-log`
38×	`associate-/r*`
34×	`div-exp`
31×	`flip3-+` `flip-+`
21×	`associate-/l*`
20×	`flip3--` `flip--`
18×	`add-cbrt-cube`
9×	`cbrt-undiv` `rec-exp` `1-exp`
7×	`pow1`
6×	`pow-unpow`
4×	`add-log-exp`
2×	`pow-to-exp` `pow-pow` `frac-2neg` `pow-exp` `clear-num`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 709

Calls

4 calls:

8.0ms	(/ 1 (- 1.0 (pow (tan x) 2)))
32.0ms	(/ (/ 1 (+ (pow (tan x) 2) 1.0)) (/ 1 (- 1.0 (pow (tan x) 2))))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series74.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (- 1.0 (pow (tan x) 2)))
31.0ms	(/ (/ 1 (+ (pow (tan x) 2) 1.0)) (/ 1 (- 1.0 (pow (tan x) 2))))
9.0ms	(pow (tan x) 2)
16.0ms	(pow (tan x) 2)

simplify202.0ms

Algorithm

egg-herbie

Counts

721 → 721

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5273	18791

prune868.0ms

Filtered

242 candidates to 721 candidates (-197.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	717	4	721
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	720	12	732

Merged error: 0.0b

Counts

732 → 12

regimes215.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	18
1	46	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

396.0ms	1493×	body	1280	valid
224.0ms	1233×	body	640	valid
179.0ms	4380×	body	80	valid
76.0ms	585×	body	320	valid
27.0ms	309×	body	160	valid

Details

analyze715.0ms

sample43.0ms

simplify541.0ms

prune4.0ms

localize10.0ms

rewrite25.0ms

series76.0ms

simplify54.0ms

prune220.0ms

localize12.0ms

rewrite42.0ms

series62.0ms

simplify89.0ms

prune341.0ms

localize10.0ms

rewrite60.0ms

series80.0ms

simplify33.0ms

prune206.0ms

localize11.0ms

rewrite104.0ms

series74.0ms

simplify202.0ms

prune868.0ms

regimes215.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling