Details

analyze718.0ms

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

13.0ms	43×	body	1280	valid
8.0ms	41×	body	640	valid
5.0ms	132×	body	80	valid
4.0ms	33×	body	320	valid
1.0ms	7×	body	160	valid

simplify458.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	15
1	16	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

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (* (tan x) (tan x)))
0.2b	(/ (- 1.0 (* (tan x) (tan x))) (+ 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:

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

series77.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- 1.0 (* (tan x) (tan x)))
32.0ms	(/ (- 1.0 (* (tan x) (tan x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(* (tan x) (tan x))
27.0ms	(* (tan x) (tan x))

simplify47.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5070	1206

prune228.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	13	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 0.0b

Counts

117 → 13

localize12.0ms

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

274×	`times-frac`
239×	`add-sqr-sqrt`
237×	`*-un-lft-identity`
113×	`add-cube-cbrt`
84×	`difference-of-squares`
46×	`associate-/r*`
41×	`distribute-lft-out`
27×	`unpow-prod-down`
23×	`unpow2` `sqr-pow`
21×	`distribute-lft-out--`
19×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
7×	`pow1` `associate-/l*`
6×	`pow-unpow` `div-inv`
5×	`flip3--` `flip--`
4×	`cbrt-undiv` `add-log-exp`
2×	`pow-to-exp` `rec-exp` `pow-pow` `frac-2neg` `1-exp` `pow-exp` `clear-num` `associate-/l/`
1×	`pow-flip` `flip3-+` `flip-+` `inv-pow`

Counts

4 → 272

Calls

4 calls:

16.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
12.0ms	(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
3.0ms	(pow (tan x) 2)
3.0ms	(pow (tan x) 2)

series85.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ 1 (/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2))))
35.0ms	(/ (+ (pow (tan x) 2) 1.0) (- 1.0 (pow (tan x) 2)))
9.0ms	(pow (tan x) 2)
9.0ms	(pow (tan x) 2)

simplify100.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5040	5487

prune441.0ms

Filtered

138 candidates to 284 candidates (-105.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	284	13	297

Merged error: 0.0b

Counts

297 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (tan x) (sin x)) (cos x))
0.2b	(* (tan x) (sin x))
0.2b	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
0.3b	(* (tan x) (tan x))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

8.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
8.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
5.0ms	(* (tan x) (tan x))

series72.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (* (tan x) (sin x)) (cos x))
10.0ms	(* (tan x) (sin x))
37.0ms	(/ (- 1.0 (/ (* (tan x) (sin x)) (cos x))) (+ 1.0 (* (tan x) (tan x))))
9.0ms	(* (tan x) (tan x))

simplify49.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5350	1680

prune157.0ms

Filtered

84 candidates to 121 candidates (-44.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	121	13	134

Merged error: 0.0b

Counts

134 → 13

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
75×	`add-sqr-sqrt`
49×	`times-frac`
30×	`add-cube-cbrt` `associate-r`
20×	`difference-of-squares`
14×	`distribute-lft-out`
12×	`add-exp-log`
11×	`add-cbrt-cube`
10×	`sqrt-prod` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `associate-l` `associate-/r*` `associate-/r/` `flip-+`
3×	`unpow-prod-down` `pow-unpow`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `-commutative` `unpow2` `sqr-pow`

Counts

4 → 137

Calls

4 calls:

4.0ms	(- (sqrt 1.0) (tan x))
11.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
23.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
3.0ms	(pow (tan x) 2)

series88.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (sqrt 1.0) (tan x))
30.0ms	(/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0))
41.0ms	(* (+ (tan x) (sqrt 1.0)) (/ (- (sqrt 1.0) (tan x)) (+ (pow (tan x) 2) 1.0)))
9.0ms	(pow (tan x) 2)

simplify65.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4971	2308
1	4971	2308

prune259.0ms

Filtered

94 candidates to 149 candidates (-58.5%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	148	14	162

Merged error: 0.0b

Counts

162 → 14

regimes158.0ms

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	12	15
1	12	15

end0.0ms

analyze517.0ms

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

sample1.1s

Algorithm

intervals

Results

407.0ms	1465×	body	1280	valid
227.0ms	1207×	body	640	valid
184.0ms	4361×	body	80	valid
82.0ms	621×	body	320	valid
35.0ms	346×	body	160	valid

Details

analyze718.0ms

sample43.0ms

simplify458.0ms

prune4.0ms

localize11.0ms

rewrite25.0ms

series77.0ms

simplify47.0ms

prune228.0ms

localize12.0ms

rewrite51.0ms

series85.0ms

simplify100.0ms

prune441.0ms

localize14.0ms

rewrite29.0ms

series72.0ms

simplify49.0ms

prune157.0ms

localize12.0ms

rewrite48.0ms

series88.0ms

simplify65.0ms

prune259.0ms

regimes158.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze517.0ms

sample1.1s

Profiling