Details

sample102.0ms

Algorithm

intervals

Results

64.0ms	166×	body	1280	valid
10.0ms	12×	body	2560	valid
10.0ms	47×	body	640	valid
4.0ms	24×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	3×	body	80	valid

simplify3.0ms

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: 39.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
3.8b	(cos (+ x eps))

rewrite10.0ms

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 → 24

Calls

2 calls:

6.0ms	(- (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))

simplify61.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4864	273
1	4864	273

prune59.0ms

Filtered

23 candidates to 30 candidates (-30.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 0.4b

Counts

31 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
3.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

14.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
5.0ms	(+ x (+ x eps))
10.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))

series34.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
4.0ms	(+ x (+ x eps))
11.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify39.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4839	890
1	4839	890

prune162.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	61	11	72
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	65	14	79

Merged error: 0.3b

Counts

79 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (sin (/ (+ x (+ x eps)) 2)))
3.9b	(sin (/ (+ x (+ x eps)) 2))
3.9b	(sin (/ (+ x (+ x eps)) 2))
3.9b	(sin (/ (+ 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:

6.0ms	(cbrt (sin (/ (+ x (+ x eps)) 2)))
7.0ms	(sin (/ (+ x (+ x eps)) 2))
7.0ms	(sin (/ (+ x (+ x eps)) 2))
7.0ms	(sin (/ (+ x (+ x eps)) 2))

series38.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify30.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5958	468

prune177.0ms

Filtered

38 candidates to 44 candidates (-15.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	12	12
Picked	1	0	1
Done	0	1	1
Total	44	14	58

Merged error: 0.3b

Counts

58 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
3.9b	(sin (/ (+ x (+ x eps)) 2))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
2.0ms	(cbrt (sin (/ eps 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

series62.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(cbrt (sin (/ eps 2)))
19.0ms	(cbrt (sin (/ eps 2)))
18.0ms	(cbrt (sin (/ eps 2)))
6.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify28.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5150	442

prune150.0ms

Filtered

45 candidates to 52 candidates (-15.6%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	49	3	52
Fresh	2	10	12
Picked	0	1	1
Done	0	1	1
Total	51	15	66

Merged error: 0.3b

Counts

66 → 15

regimes255.0ms

Accuracy

97.1% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 15.3b

bsearch75.0ms

Steps

Iters	Range		Point
9	5.637513820892623e-10	0.06592465963988953	1.0227397076061673e-05
7	-167.22532332526734	-0.6973264211480649	-0.7127791457499839

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	38
1	35	38

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4509×	body	1280	valid
575.0ms	613×	body	2560	valid
436.0ms	1852×	body	640	valid
103.0ms	651×	body	320	valid
31.0ms	290×	body	160	valid
5.0ms	85×	body	80	valid

Details

sample102.0ms

simplify3.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series14.0ms

simplify61.0ms

prune59.0ms

localize13.0ms

rewrite36.0ms

series34.0ms

simplify39.0ms

prune162.0ms

localize16.0ms

rewrite26.0ms

series38.0ms

simplify30.0ms

prune177.0ms

localize16.0ms

rewrite13.0ms

series62.0ms

simplify28.0ms

prune150.0ms

regimes255.0ms

bsearch75.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling