Details

analyze864.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample89.0ms

Algorithm

intervals

Results

40.0ms	108×	body	1280	valid
18.0ms	61×	body	640	valid
16.0ms	19×	body	2560	valid
3.0ms	23×	body	320	valid
2.0ms	37×	body	80	valid
1.0ms	8×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

prune3.0ms

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: 35.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.7b	(- (tan (+ x eps)) (tan x))
3.2b	(tan (+ x eps))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`tan-quot` `add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `tan-sum` `frac-sub` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

6.0ms	(- (tan (+ x eps)) (tan x))
3.0ms	(tan (+ x eps))

series42.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(- (tan (+ x eps)) (tan x))
16.0ms	(tan (+ x eps))

simplify112.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4868	332
1	4868	332

prune63.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	21	9	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	9	31

Merged error: 16.0b

Counts

31 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1 (* (tan x) (tan eps)))
0.1b	(+ (tan x) (tan eps))
0.2b	(* (tan x) (tan eps))
2.6b	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`tan-quot`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l`
2×	`sub-neg` `flip3--` `diff-log` `flip--` `difference-of-squares`
1×	`+-commutative` `frac-times` `flip3-+` `times-frac` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `sum-log` `*-commutative` `frac-sub` `cbrt-unprod` `flip-+` `distribute-lft-out` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

3.0ms	(- 1 (* (tan x) (tan eps)))
4.0ms	(+ (tan x) (tan eps))
5.0ms	(* (tan x) (tan eps))
11.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(- 1 (* (tan x) (tan eps)))
20.0ms	(+ (tan x) (tan eps))
21.0ms	(* (tan x) (tan eps))
142.0ms	(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

simplify58.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4982	963
1	4982	963

prune146.0ms

Filtered

55 candidates to 72 candidates (-30.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	58	14	72
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	65	16	81

Merged error: 15.9b

Counts

81 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (tan x) (tan eps))
0.2b	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
0.3b	(* (tan eps) (tan eps))
2.6b	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

41×	`tan-quot`
24×	`add-sqr-sqrt`
22×	`pow1`
19×	`frac-times` `associate-*r/`
17×	`add-exp-log` `add-cbrt-cube`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`associate-l` `associate-*l/`
8×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`associate-r`
6×	`add-log-exp`
3×	`times-frac` `swap-sqr` `*-commutative` `difference-of-squares`
2×	`unswap-sqr`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `pow-sqr` `pow-prod-up` `frac-sub` `flip--` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

5.0ms	(* (tan x) (tan eps))
11.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
5.0ms	(* (tan eps) (tan eps))
26.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))

series383.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (tan x) (tan eps))
30.0ms	(* (tan x) (* (tan x) (* (tan eps) (tan eps))))
8.0ms	(* (tan eps) (tan eps))
321.0ms	(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (tan x) (* (tan x) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))))) (tan x))

simplify42.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5635	1730

prune155.0ms

Filtered

73 candidates to 113 candidates (-54.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	109	4	113
Fresh	10	5	15
Picked	1	0	1
Done	0	0	0
Total	120	9	129

Merged error: 0.2b

Counts

129 → 9

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin eps) 2)
0.3b	(pow (sin eps) 2)
0.3b	(pow (sin eps) 2)
1.6b	(- (* (+ (/ (pow (sin eps) 2) (pow (cos eps) 2)) 1) (/ (sin x) (* (cos x) (- 1 (* (/ (pow (sin eps) 2) (pow (cos eps) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (sin x) (cos x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
5×	`frac-sub`
4×	`add-cbrt-cube`
3×	`pow-to-exp` `pow-pow` `pow-exp` `unpow2` `sqr-pow`
2×	`frac-times` `flip3-+` `associate-*l/` `flip-+`
1×	`sub-neg` `flip3--` `diff-log` `associate-*r/` `flip--`

Counts

4 → 70

Calls

4 calls:

3.0ms	(pow (sin eps) 2)
3.0ms	(pow (sin eps) 2)
3.0ms	(pow (sin eps) 2)
32.0ms	(- (* (+ (/ (pow (sin eps) 2) (pow (cos eps) 2)) 1) (/ (sin x) (* (cos x) (- 1 (* (/ (pow (sin eps) 2) (pow (cos eps) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (sin x) (cos x)))

series187.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (sin eps) 2)
3.0ms	(pow (sin eps) 2)
3.0ms	(pow (sin eps) 2)
176.0ms	(- (* (+ (/ (pow (sin eps) 2) (pow (cos eps) 2)) 1) (/ (sin x) (* (cos x) (- 1 (* (/ (pow (sin eps) 2) (pow (cos eps) 2)) (/ (pow (sin x) 2) (pow (cos x) 2))))))) (/ (sin x) (cos x)))

simplify58.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4973	1556
1	4973	1556

prune301.0ms

Filtered

52 candidates to 82 candidates (-57.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Merged error: 0.2b

Counts

91 → 10

regimes156.0ms

Accuracy

0% (0.4b remaining)

Error of 0.7b against oracle of 0.3b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	87
1	38	87

end0.0ms

analyze785.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample2.7s

Algorithm

intervals

Results

1.3s	3268×	body	1280	valid
585.0ms	669×	body	2560	valid
416.0ms	1861×	body	640	valid
105.0ms	742×	body	320	valid
48.0ms	1091×	body	80	valid
38.0ms	369×	body	160	valid

Details

analyze864.0ms

sample89.0ms

simplify2.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series42.0ms

simplify112.0ms

prune63.0ms

localize13.0ms

rewrite23.0ms

series209.0ms

simplify58.0ms

prune146.0ms

localize17.0ms

rewrite50.0ms

series383.0ms

simplify42.0ms

prune155.0ms

localize35.0ms

rewrite41.0ms

series187.0ms

simplify58.0ms

prune301.0ms

regimes156.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze785.0ms

sample2.7s

Profiling