Details

sample29.0ms

Algorithm

intervals

Results

14.0ms	91×	body	1280	valid
5.0ms	140×	body	80	valid
2.0ms	15×	body	640	valid
0.0ms	6×	body	160	valid
0.0ms	4×	body	320	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

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: 13.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
10.0ms	(- (atan (+ N 1.0)) (atan N))

simplify76.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune43.0ms

Filtered

28 candidates to 19 candidates (67.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	2	29

Merged error: 0.2b

Counts

29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite7.0ms

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:

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

series42.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify59.0ms

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

prune51.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	28	8	36

Merged error: 0.1b

Counts

36 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.5b	(cbrt N)
0.5b	(cbrt N)
0.5b	(cbrt N)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

10.0ms	(* (cbrt N) (cbrt N))
2.0ms	(cbrt N)
2.0ms	(cbrt N)
2.0ms	(cbrt N)

series757.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (cbrt N) (cbrt N))
184.0ms	(cbrt N)
171.0ms	(cbrt N)
204.0ms	(cbrt N)

simplify89.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune237.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	85	8	93

Merged error: 0.1b

Counts

93 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))
0.3b	(cbrt (+ N 1.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

10.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))

series372.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
85.0ms	(cbrt (+ N 1.0))
85.0ms	(cbrt (+ N 1.0))
92.0ms	(cbrt (+ N 1.0))

simplify178.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (166.0ms)

Iter	Nodes	Cost
0	305	792
1	999	747
2	4427	693
3	5001	689

prune213.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	4	4
Picked	1	0	1
Done	0	3	3
Total	107	8	115

Merged error: 0.1b

Counts

115 → 8

regimes52.0ms

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

sample830.0ms

Algorithm

intervals

Results

458.0ms	2918×	body	1280	valid
142.0ms	3984×	body	80	valid
80.0ms	612×	body	640	valid
31.0ms	314×	body	320	valid
12.0ms	172×	body	160	valid

Details

sample29.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series11.0ms

simplify76.0ms

prune43.0ms

localize6.0ms

rewrite7.0ms

series42.0ms

simplify59.0ms

prune51.0ms

localize17.0ms

rewrite19.0ms

series757.0ms

simplify89.0ms

prune237.0ms

localize9.0ms

rewrite22.0ms

series372.0ms

simplify178.0ms

prune213.0ms

regimes52.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample830.0ms

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