Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	85×	body	1280	valid
5.0ms	127×	body	80	valid
4.0ms	30×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 18.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.0b	(- (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 → 22

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))

simplify74.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2447	142
5	5001	142

prune41.0ms

Filtered

28 candidates to 19 candidates (32.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	3	29

Merged error: 0.7b

Counts

29 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1 (* (+ N 1.0) N))
0.0b	(* (+ N 1.0) N)
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 39

Calls

3 calls:

3.0ms	(+ 1 (* (+ N 1.0) N))
6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series9.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify115.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	177	222
1	766	193
2	4572	193
3	5001	193

prune72.0ms

Filtered

48 candidates to 32 candidates (33.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	43	8	51

Merged error: 0.7b

Counts

51 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
13.7b	(cbrt (* (+ N 1.0) N))
13.7b	(cbrt (* (+ N 1.0) N))
13.7b	(cbrt (* (+ N 1.0) N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 40

Calls

4 calls:

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

series30.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
9.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))

simplify57.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	207	623
1	572	575
2	1929	533
3	5001	525

prune157.0ms

Filtered

52 candidates to 47 candidates (9.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	52	8	60

Merged error: 0.7b

Counts

60 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
12.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
12.4b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite4.0ms

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))))

simplify74.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	49	332
1	79	294
2	159	294
3	330	292
4	1184	292
5	5001	292

prune87.0ms

Filtered

52 candidates to 34 candidates (34.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	52	8	60

Merged error: 0.7b

Counts

60 → 8

regimes85.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample826.0ms

Algorithm

intervals

Results

429.0ms	2884×	body	1280	valid
143.0ms	4046×	body	80	valid
71.0ms	591×	body	640	valid
28.0ms	299×	body	320	valid
12.0ms	180×	body	160	valid

Details

sample29.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify74.0ms

prune41.0ms

localize6.0ms

rewrite10.0ms

series9.0ms

simplify115.0ms

prune72.0ms

localize10.0ms

rewrite15.0ms

series30.0ms

simplify57.0ms

prune157.0ms

localize10.0ms

rewrite4.0ms

series16.0ms

simplify74.0ms

prune87.0ms

regimes85.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample826.0ms

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