Details

sample26.0ms

Algorithm

intervals

Results

13.0ms	94×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	4×	body	160	valid

simplify5.0ms

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 (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite3.0ms

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:

0.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify72.0ms

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	2491	142
5	5001	142

prune51.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.8b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

10.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series50.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify52.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune61.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
16.3b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.3b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite2.0ms

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:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.0ms	(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))))

series37.0ms

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)))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
18.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify72.0ms

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	1202	292
5	5002	292

prune108.0ms

Filtered

52 candidates to 34 candidates (65.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
16.3b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.3b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
16.3b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 46

Calls

4 calls:

0.0ms	(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))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series47.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify77.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	49	368
1	79	335
2	159	335
3	330	332
4	1202	332
5	5002	332

prune140.0ms

Filtered

58 candidates to 37 candidates (63.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.7b

regimes30.0ms

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

sample747.0ms

Algorithm

intervals

Results

410.0ms	2887×	body	1280	valid
131.0ms	4093×	body	80	valid
68.0ms	595×	body	640	valid
24.0ms	273×	body	320	valid
10.0ms	152×	body	160	valid