Details

analyze695.0ms

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

15.0ms	58×	body	1280	valid
10.0ms	34×	body	640	valid
6.0ms	138×	body	80	valid
3.0ms	22×	body	320	valid
0.0ms	4×	body	160	valid

simplify533.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

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: 0.4b

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))))
0.2b	(- 1.0 (* (tan x) (tan x)))
0.2b	(* (tan x) (tan x))
0.2b	(* (tan x) (tan x))

rewrite33.0ms

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:

15.0ms	(/ (- 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))

series66.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(- 1.0 (* (tan x) (tan x)))
8.0ms	(* (tan x) (tan x))
18.0ms	(* (tan x) (tan x))

simplify53.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune224.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

292×	`*-un-lft-identity`
264×	`times-frac`
204×	`add-sqr-sqrt`
104×	`add-cube-cbrt`
69×	`distribute-lft-out`
50×	`difference-of-squares`
36×	`associate-/r*`
25×	`sqrt-prod` `distribute-lft-out--`
13×	`associate-/r/`
12×	`add-exp-log`
11×	`add-cbrt-cube`
8×	`associate-/l*`
7×	`div-inv`
6×	`flip3--` `flip--` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`unpow-prod-down` `pow-unpow` `flip3-+` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow-exp` `sum-log` `unpow2` `sqr-pow`

Counts

4 → 251

Calls

4 calls:

19.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x))))
11.0ms	(/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x)))
3.0ms	(pow (tan x) 2)
4.0ms	(+ (sqrt 1.0) (tan x))

series81.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (+ (sqrt 1.0) (tan x)) (/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x))))
23.0ms	(/ (+ (pow (tan x) 2) 1.0) (- (sqrt 1.0) (tan x)))
8.0ms	(pow (tan x) 2)
11.0ms	(+ (sqrt 1.0) (tan x))

simplify91.0ms

Algorithm

egg-herbie

Counts

263 → 263

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4987	6416
1	4987	6416

prune492.0ms

Filtered

143 candidates to 263 candidates (-83.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	261	2	263
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	261	14	275

Merged error: 0.1b

Counts

275 → 14

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

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:

16.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
5.0ms	(- 1.0 (pow (tan x) 2))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series55.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
8.0ms	(- 1.0 (pow (tan x) 2))
8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)

simplify88.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4972	4413
1	4972	4413

prune337.0ms

Filtered

114 candidates to 240 candidates (-110.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	241	13	254

Merged error: 0.1b

Counts

254 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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)
41.0ms	(- (/ 1.0 (+ (pow (tan x) 2) 1.0)) (/ (pow (tan x) 2) (+ (pow (tan x) 2) 1.0)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)
8.0ms	(pow (tan x) 2)
51.0ms	(- (/ 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 (23.0ms)

Iter	Nodes	Cost
0	5194	1408

prune167.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	5	6	11
Picked	1	0	1
Done	0	1	1
Total	100	12	112

Merged error: 0.0b

Counts

112 → 12

regimes150.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	23	18
1	23	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

408.0ms	1594×	body	1280	valid
214.0ms	1302×	body	640	valid
160.0ms	4193×	body	80	valid
73.0ms	621×	body	320	valid
24.0ms	290×	body	160	valid

Details

analyze695.0ms

sample43.0ms

simplify533.0ms

prune4.0ms

localize10.0ms

rewrite33.0ms

series66.0ms

simplify53.0ms

prune224.0ms

localize11.0ms

rewrite52.0ms

series81.0ms

simplify91.0ms

prune492.0ms

localize9.0ms

rewrite41.0ms

series55.0ms

simplify88.0ms

prune337.0ms

localize12.0ms

rewrite52.0ms

series76.0ms

simplify33.0ms

prune167.0ms

regimes150.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling