Details

sample107.0ms

Algorithm

intervals

Results

51.0ms	120×	body	1280	valid
15.0ms	19×	body	2560	valid
15.0ms	56×	body	640	valid
10.0ms	28×	body	320	valid
2.0ms	27×	body	80	valid
1.0ms	6×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	7
1	10	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: 36.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (sin (+ x eps)) (sin x))
3.5b	(sin (+ x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

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

series15.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(- (sin (+ x eps)) (sin x))
6.0ms	(sin (+ x eps))

simplify46.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5225	271

prune51.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	27	3	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	3	31

Merged error: 0.5b

Counts

31 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
3.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite21.0ms

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` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

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

series26.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ x (+ x eps))
12.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
9.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify47.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5118	541

prune123.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	44	9	53

Merged error: 0.4b

Counts

53 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 32

Calls

4 calls:

1.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
8.0ms	(cos (/ (+ x (+ x eps)) 2))
8.0ms	(cos (/ (+ x (+ x eps)) 2))
8.0ms	(cos (/ (+ x (+ x eps)) 2))

series37.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
6.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify33.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5689	447

prune173.0ms

Filtered

37 candidates to 44 candidates (-18.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	42	2	44
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	44	9	53

Merged error: 0.4b

Counts

53 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))
3.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`

Counts

4 → 28

Calls

4 calls:

9.0ms	(cos (/ (+ x (+ x eps)) 2))
10.0ms	(cos (/ (+ x (+ x eps)) 2))
8.0ms	(cos (/ (+ x (+ x eps)) 2))
8.0ms	(cos (/ (+ x (+ x eps)) 2))

series23.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5258	380

prune183.0ms

Filtered

36 candidates to 40 candidates (-11.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	40	9	49

Merged error: 0.4b

Counts

49 → 9

regimes172.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.9b

bsearch59.0ms

Steps

Iters	Range		Point
8	5.972365790103743e-15	5.691295351696058e-12	5.621069998466474e-12
5	-0.0004813576712207844	-0.0001616040529746431	-0.0001647469450861392

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	38
1	35	38

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.4s	3317×	body	1280	valid
574.0ms	668×	body	2560	valid
480.0ms	1800×	body	640	valid
143.0ms	749×	body	320	valid
68.0ms	1117×	body	80	valid
49.0ms	349×	body	160	valid

Details

sample107.0ms

simplify2.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series15.0ms

simplify46.0ms

prune51.0ms

localize13.0ms

rewrite21.0ms

series26.0ms

simplify47.0ms

prune123.0ms

localize17.0ms

rewrite26.0ms

series37.0ms

simplify33.0ms

prune173.0ms

localize21.0ms

rewrite35.0ms

series23.0ms

simplify53.0ms

prune183.0ms

regimes172.0ms

bsearch59.0ms

simplify1.0ms

end0.0ms

sample3.0s

Profiling