Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	93×	body	1280	valid
4.0ms	127×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	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: 14.7b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.9b	(- (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))

simplify75.0ms

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

prune52.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite13.0ms

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:

12.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series43.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

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

prune64.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series532.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (* (cbrt N) (cbrt N))) (cbrt N))))
179.0ms	(cbrt N)
173.0ms	(cbrt N)
175.0ms	(cbrt N)

simplify86.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (82.0ms)

Iter	Nodes	Cost
0	75	232
1	164	204
2	534	198
3	2409	194
4	5001	191

prune139.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt (cbrt N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
9×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 47

Calls

4 calls:

0.0ms	(cbrt N)
0.0ms	(cbrt N)
0.0ms	(cbrt N)
1.0ms	(cbrt (cbrt N))

series950.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(cbrt N)
363.0ms	(cbrt N)
176.0ms	(cbrt N)
239.0ms	(cbrt (cbrt N))

simplify48.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	71	191
1	141	177
2	357	169
3	1377	169
4	5001	169

prune195.0ms

Filtered

59 candidates to 52 candidates (88.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.5b

regimes29.0ms

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	12	4
1	12	4

end0.0ms

sample741.0ms

Algorithm

intervals

Results

397.0ms	2812×	body	1280	valid
126.0ms	4109×	body	80	valid
77.0ms	606×	body	640	valid
29.0ms	324×	body	320	valid
10.0ms	149×	body	160	valid