Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample32.0ms

Algorithm

intervals

Results

15.0ms	104×	body	1280	valid
4.0ms	127×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	1×	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: 13.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.7b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

series4.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (atan (+ N 1.0)) (atan N))

simplify67.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5349	236

prune35.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	1	28

Merged error: 0.5b

Counts

28 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.5b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-r` `add-cbrt-cube`
3×	`associate-l`
2×	`associate-*r/` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 30

Calls

2 calls:

9.0ms	(* N (+ N 1.0))
1.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

series6.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* N (+ N 1.0))
2.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune57.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	4	37

Merged error: 0.4b

Counts

37 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
16.7b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.7b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
6.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
2.0ms	(* (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))) (sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N))))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify48.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5253	989

prune137.0ms

Filtered

47 candidates to 94 candidates (-100.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	90	4	94
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	90	8	98

Merged error: 0.4b

Counts

98 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.5b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
16.7b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.7b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 40

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
1.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

series17.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
2.0ms	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
6.0ms	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

simplify59.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4899	570
1	4899	570

prune116.0ms

Filtered

34 candidates to 52 candidates (-52.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	53	7	60

Merged error: 0.4b

Counts

60 → 7

regimes46.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

sample794.0ms

Algorithm

intervals

Results

430.0ms	2851×	body	1280	valid
141.0ms	4053×	body	80	valid
81.0ms	628×	body	640	valid
30.0ms	311×	body	320	valid
11.0ms	157×	body	160	valid

Details

analyze1.0ms

sample32.0ms

simplify4.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series4.0ms

simplify67.0ms

prune35.0ms

localize6.0ms

rewrite10.0ms

series6.0ms

simplify60.0ms

prune57.0ms

localize9.0ms

rewrite12.0ms

series17.0ms

simplify48.0ms

prune137.0ms

localize11.0ms

rewrite5.0ms

series17.0ms

simplify59.0ms

prune116.0ms

regimes46.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample794.0ms

Profiling