Details

analyze2.0ms

Algorithm

Search

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

sample104.0ms

Algorithm

intervals

Results

51.0ms	104×	body	1280	valid
22.0ms	23×	body	2560	valid
16.0ms	60×	body	640	valid
3.0ms	16×	body	320	valid
3.0ms	41×	body	80	valid
2.0ms	12×	body	160	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: 38.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
4.0b	(sin (+ 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` `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:

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(- (sin (+ x eps)) (sin x))
4.0ms	(sin (+ x eps))

simplify42.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5348	268

prune46.0ms

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: 0.3b

Counts

30 → 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)))
3.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite17.0ms

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

series21.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5169	541

prune109.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	8	53

Merged error: 0.3b

Counts

53 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
0.5b	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
0.5b	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
3.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod`
24×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
10×	`unpow-prod-down` `cube-prod`
7×	`pow1` `add-exp-log`
6×	`add-cbrt-cube`
5×	`unswap-sqr`
4×	`add-log-exp` `sqr-pow`
3×	`cube-mult` `pow-unpow` `unpow3` `associate-l`
1×	`pow-to-exp` `pow-pow` `pow1/3` `pow-prod-down` `pow-exp` `prod-exp` `*-commutative` `rem-cbrt-cube` `cbrt-unprod` `rem-cube-cbrt`

Counts

4 → 85

Calls

4 calls:

8.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
2.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
2.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series32.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3)))
12.0ms	(pow (cos (/ (+ x (+ x eps)) 2)) 3)
5.0ms	(cbrt (pow (cos (/ (+ x (+ x eps)) 2)) 3))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify40.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4924	1255
1	4924	1255

prune153.0ms

Filtered

55 candidates to 97 candidates (-76.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Merged error: 0.3b

Counts

105 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (cos (/ (+ x (+ x eps)) 2)))
3.9b	(cos (/ (+ x (+ x eps)) 2))
3.9b	(cos (/ (+ x (+ x eps)) 2))
3.9b	(cos (/ (+ x (+ x eps)) 2))

rewrite23.0ms

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))
6.0ms	(cos (/ (+ x (+ x eps)) 2))
7.0ms	(cos (/ (+ x (+ x eps)) 2))

series31.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(cbrt (cos (/ (+ x (+ x eps)) 2)))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))
5.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify69.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4872	415
1	4872	415

prune116.0ms

Filtered

37 candidates to 44 candidates (-18.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	44	8	52

Merged error: 0.3b

Counts

52 → 8

regimes163.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.4b and baseline of 14.6b

bsearch77.0ms

Steps

Iters	Range		Point
10	2.3371078394277945e-18	8.187469366386551e-08	1.7904989265996457e-08
8	-31.653317132880385	-0.004380114327240192	-0.004478205628609146

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3216×	body	1280	valid
623.0ms	641×	body	2560	valid
516.0ms	1877×	body	640	valid
147.0ms	770×	body	320	valid
67.0ms	1138×	body	80	valid
49.0ms	358×	body	160	valid

Details

analyze2.0ms

sample104.0ms

simplify4.0ms

prune3.0ms

localize8.0ms

rewrite10.0ms

series12.0ms

simplify42.0ms

prune46.0ms

localize13.0ms

rewrite17.0ms

series21.0ms

simplify54.0ms

prune109.0ms

localize15.0ms

rewrite20.0ms

series32.0ms

simplify40.0ms

prune153.0ms

localize18.0ms

rewrite23.0ms

series31.0ms

simplify69.0ms

prune116.0ms

regimes163.0ms

bsearch77.0ms

simplify1.0ms

end0.0ms

sample3.1s

Profiling