Details

analyze702.0ms

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

sample57.0ms

Algorithm

intervals

Results

13.0ms	49×	body	1280	valid
8.0ms	44×	body	640	valid
5.0ms	139×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	10×	body	160	valid

simplify520.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	5284	15

prune19.0ms

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))))
0.2b	(- 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))

series70.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (- 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))

simplify54.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune227.0ms

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: 0.1b

Counts

117 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (cos x) 2)
0.3b	(pow (cos x) 2)
0.3b	(pow (sin x) 2)
0.3b	(pow (sin x) 2)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `pow-unpow` `*-un-lft-identity`
8×	`pow1` `add-exp-log`
4×	`pow-to-exp` `pow-pow` `pow-exp` `add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

2.0ms	(pow (cos x) 2)
2.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

series15.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (cos x) 2)
5.0ms	(pow (cos x) 2)
3.0ms	(pow (sin x) 2)
3.0ms	(pow (sin x) 2)

simplify38.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5266	424

prune155.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.1b

Counts

97 → 12

localize10.0ms

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))
0.3b	(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:

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)
5.0ms	(pow (tan x) 2)

series59.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 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)

simplify87.0ms

Algorithm

egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4972	4413
1	4972	4413

prune338.0ms

Filtered

113 candidates to 240 candidates (-112.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	237	3	240
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	238	14	252

Merged error: 0.1b

Counts

252 → 14

localize15.0ms

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)))
0.3b	(* (tan x) (tan x))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

6.0ms	(/ (* (tan x) (sin x)) (cos x))
5.0ms	(* (tan x) (sin x))
5.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
5.0ms	(* (tan x) (tan x))

series49.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ (* (tan x) (sin x)) (cos x))
10.0ms	(* (tan x) (sin x))
16.0ms	(- 1.0 (/ (* (tan x) (sin x)) (cos x)))
8.0ms	(* (tan x) (tan x))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	791
1	4977	791

prune87.0ms

Filtered

62 candidates to 94 candidates (-51.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	10	12
Picked	0	1	1
Done	1	0	1
Total	95	13	108

Merged error: 0.0b

Counts

108 → 13

regimes214.0ms

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

sample1.4s

Algorithm

intervals

Results

356.0ms	1431×	body	1280	valid
211.0ms	1289×	body	640	valid
151.0ms	4364×	body	80	valid
72.0ms	618×	body	320	valid
24.0ms	298×	body	160	valid

Details

analyze702.0ms

sample57.0ms

simplify520.0ms

prune19.0ms

localize10.0ms

rewrite25.0ms

series70.0ms

simplify54.0ms

prune227.0ms

localize14.0ms

rewrite11.0ms

series15.0ms

simplify38.0ms

prune155.0ms

localize10.0ms

rewrite42.0ms

series59.0ms

simplify87.0ms

prune338.0ms

localize15.0ms

rewrite22.0ms

series49.0ms

simplify52.0ms

prune87.0ms

regimes214.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling