Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample100.0ms

Algorithm

intervals

Results

58.0ms	147×	body	1280	valid
16.0ms	67×	body	640	valid
14.0ms	16×	body	2560	valid
3.0ms	17×	body	320	valid
1.0ms	7×	body	160	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	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: 40.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 23

Calls

2 calls:

7.0ms	(- (cos (+ x eps)) (cos x))
4.0ms	(cos (+ x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (cos (+ x eps)) (cos x))
5.0ms	(cos (+ x eps))

simplify24.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4999	270
1	4999	270

prune58.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	6	30

Merged error: 0.3b

Counts

30 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
2.5b	(sin (/ (+ x (+ x eps)) 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+r+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

6.0ms	(+ x (+ x eps))
11.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
9.0ms	(sin (/ (+ x (+ x eps)) 2))

series22.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ x eps))
12.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify50.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5025	543

prune116.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	46	10	56

Merged error: 0.2b

Counts

56 → 10

localize11.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
2.5b	(sin (+ x (* eps 1/2)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`sin-sum` `associate-r` `associate-l`
2×	`add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

2 → 29

Calls

2 calls:

8.0ms	(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
4.0ms	(sin (+ x (* eps 1/2)))

series17.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(* (sin (/ eps 2)) (sin (+ x (* eps 1/2))))
5.0ms	(sin (+ x (* eps 1/2)))

simplify59.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4785	432
1	4785	432

prune106.0ms

Filtered

28 candidates to 35 candidates (-25.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	27	8	35
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	34	11	45

Merged error: 0.1b

Counts

45 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* eps 1/2)) (sin (/ eps 2)))
0.2b	(* (cos x) (* (sin (* eps 1/2)) (sin (/ eps 2))))
0.2b	(* (sin x) (* (cos (* eps 1/2)) (sin (/ eps 2))))
0.2b	(* (sin (* eps 1/2)) (sin (/ eps 2)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`associate-l`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`*-commutative` `add-log-exp`
2×	`sin-mult` `unswap-sqr`
1×	`associate-*r/`

Counts

4 → 74

Calls

4 calls:

5.0ms	(* (cos (* eps 1/2)) (sin (/ eps 2)))
8.0ms	(* (cos x) (* (sin (* eps 1/2)) (sin (/ eps 2))))
8.0ms	(* (sin x) (* (cos (* eps 1/2)) (sin (/ eps 2))))
6.0ms	(* (sin (* eps 1/2)) (sin (/ eps 2)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* (cos (* eps 1/2)) (sin (/ eps 2)))
12.0ms	(* (cos x) (* (sin (* eps 1/2)) (sin (/ eps 2))))
17.0ms	(* (sin x) (* (cos (* eps 1/2)) (sin (/ eps 2))))
4.0ms	(* (sin (* eps 1/2)) (sin (/ eps 2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4944	880
1	4944	880

prune181.0ms

Filtered

66 candidates to 86 candidates (-30.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

regimes187.0ms

Accuracy

71.2% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 4.0b

bsearch90.0ms

Steps

Iters	Range		Point
8	7.68848971492884e-73	3.040507251683647e-69	6.203423099167994e-72
7	-1.2203975847718485e-123	-4.610186334894915e-125	-2.320785422446366e-124

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	63
1	45	63

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.7s	4507×	body	1280	valid
577.0ms	634×	body	2560	valid
401.0ms	1796×	body	640	valid
103.0ms	672×	body	320	valid
33.0ms	304×	body	160	valid
5.0ms	87×	body	80	valid

Details

analyze2.0ms

sample100.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite11.0ms

series14.0ms

simplify24.0ms

prune58.0ms

localize13.0ms

rewrite27.0ms

series22.0ms

simplify50.0ms

prune116.0ms

localize11.0ms

rewrite12.0ms

series17.0ms

simplify59.0ms

prune106.0ms

localize24.0ms

rewrite29.0ms

series37.0ms

simplify69.0ms

prune181.0ms

regimes187.0ms

bsearch90.0ms

simplify1.0ms

end0.0ms

sample3.0s

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