Details

analyze1.0ms

Algorithm

Search

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

sample29.0ms

Algorithm

intervals

Results

15.0ms	98×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	14×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	5×	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: 14.0b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.4b	(- (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))

series3.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

simplify67.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5349	236

prune39.0ms

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: 0.4b

Counts

28 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 7

Calls

1 calls:

1.0ms

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

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

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

simplify125.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4712	109
1	4712	109

prune27.0ms

Filtered

8 candidates to 10 candidates (-25.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	7	4	11

Merged error: 0.4b

Counts

11 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.4b	(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))))))
16.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))

rewrite11.0ms

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)))))

simplify45.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5253	989

prune131.0ms

Filtered

46 candidates to 94 candidates (-104.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	93	5	98

Merged error: 0.4b

Counts

98 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
0.4b	(atan2 1.0 (+ 1 (* N (+ 1.0 N))))
16.0b	(sqrt (atan2 1.0 (+ 1 (* N (+ 1.0 N)))))
16.0b	(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)))))

series16.0ms

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)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4899	570
1	4899	570

prune118.0ms

Filtered

34 candidates to 52 candidates (-52.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	50	7	57

Merged error: 0.4b

Counts

57 → 7

regimes52.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	9
1	11	9

end0.0ms

sample810.0ms

Algorithm

intervals

Results

443.0ms	2844×	body	1280	valid
143.0ms	4114×	body	80	valid
78.0ms	595×	body	640	valid
33.0ms	305×	body	320	valid
11.0ms	142×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify4.0ms

prune3.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify67.0ms

prune39.0ms

localize6.0ms

rewrite1.0ms

series2.0ms

simplify125.0ms

prune27.0ms

localize8.0ms

rewrite11.0ms

series17.0ms

simplify45.0ms

prune131.0ms

localize13.0ms

rewrite5.0ms

series16.0ms

simplify57.0ms

prune118.0ms

regimes52.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample810.0ms

Profiling