Details

analyze1.0ms

Algorithm

Search

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

sample317.0ms

Algorithm

intervals

Results

49.0ms	108×	body	1280	valid
22.0ms	23×	body	2560	valid
14.0ms	56×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	16×	body	160	valid
2.0ms	34×	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: 36.3b

Counts

2 → 1

localize66.0ms

Local error

Found 2 expressions with local error:

14.4b	(sin (+ x eps))
21.7b	(- (sin (+ x eps)) (sin x))

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` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 23

Calls

2 calls:

4.0ms	(sin (+ x eps))
6.0ms	(- (sin (+ x eps)) (sin x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(sin (+ x eps))
9.0ms	(- (sin (+ x eps)) (sin x))

simplify43.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5348	268

prune47.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.2b

Counts

30 → 3

localize66.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ x eps))
0.2b	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
14.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite19.0ms

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:

5.0ms	(+ x (+ x eps))
5.0ms	(* (sin (/ eps 2)) (cos (/ (+ x (+ x eps)) 2)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series23.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5169	541

prune97.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	47	3	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	47	6	53

Merged error: 0.2b

Counts

53 → 6

localize73.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
14.7b	(cos (/ (+ x (+ x eps)) 2))
14.7b	(cos (/ (+ x (+ x eps)) 2))
14.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite22.0ms

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)))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series34.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
6.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4872	415
1	4872	415

prune154.0ms

Filtered

37 candidates to 44 candidates (-18.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	42	8	50

Merged error: 0.2b

Counts

50 → 8

localize77.0ms

Local error

Found 4 expressions with local error:

0.6b	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
14.7b	(cos (/ (+ x (+ x eps)) 2))
14.7b	(cos (/ (+ x (+ x eps)) 2))
14.7b	(cos (/ (+ x (+ x eps)) 2))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod`
1×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 44

Calls

4 calls:

2.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
9.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series28.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify40.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5073	552

prune150.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	56	8	64

Merged error: 0.2b

Counts

64 → 8

regimes187.0ms

Accuracy

97.6% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.9b

bsearch183.0ms

Steps

Iters	Range		Point
8	2.378184767192916e-12	1.1266294431677668e-08	1.1088692445762939e-08
9	-4180579059620742.5	-9176798620.626127	-9334405717.835932

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	38
1	45	38

end0.0ms

sample8.4s

Algorithm

intervals

Results

1.4s	3231×	body	1280	valid
622.0ms	653×	body	2560	valid
468.0ms	1826×	body	640	valid
144.0ms	813×	body	320	valid
66.0ms	1111×	body	80	valid
42.0ms	366×	body	160	valid

Details

analyze1.0ms

sample317.0ms

simplify4.0ms

prune3.0ms

localize66.0ms

rewrite10.0ms

series13.0ms

simplify43.0ms

prune47.0ms

localize66.0ms

rewrite19.0ms

series23.0ms

simplify55.0ms

prune97.0ms

localize73.0ms

rewrite22.0ms

series34.0ms

simplify68.0ms

prune154.0ms

localize77.0ms

rewrite26.0ms

series28.0ms

simplify40.0ms

prune150.0ms

regimes187.0ms

bsearch183.0ms

simplify2.0ms

end0.0ms

sample8.4s

Profiling