Details

sample27.0ms

Algorithm

intervals

Results

12.0ms	85×	body	1280	valid
4.0ms	128×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	7×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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: 18.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.8b	(- (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))
4.0ms	(- (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))

simplify85.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (13.0ms)

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

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.6b

Counts

29 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite8.0ms

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)))

series45.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify69.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (6.0ms)

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

prune66.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	27	7	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	27	8	35

Merged error: 0.5b

Counts

35 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

39×	`cbrt-prod`
19×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`add-cube-cbrt`
12×	`associate-l`
9×	`associate-r`
6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`flip3-+` `pow1/3` `*-commutative` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

4 → 76

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series333.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
113.0ms	(cbrt (* (+ N 1.0) N))
110.0ms	(cbrt (* (+ N 1.0) N))
103.0ms	(cbrt (* (+ N 1.0) N))

simplify99.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (90.0ms)

Iter	Nodes	Cost
0	240	809
1	712	761
2	3007	719
3	5001	702

prune283.0ms

Filtered

88 candidates to 71 candidates (80.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	88	8	96

Merged error: 0.5b

Counts

96 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))
13.1b	(cbrt (* (+ N 1.0) N))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

52×	`cbrt-prod`
24×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`add-cube-cbrt` `associate-l`
12×	`associate-r`
8×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `flip3-+` `pow1/3` `*-commutative` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))
7.0ms	(cbrt (* (+ N 1.0) N))

series420.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(cbrt (* (+ N 1.0) N))
102.0ms	(cbrt (* (+ N 1.0) N))
103.0ms	(cbrt (* (+ N 1.0) N))
103.0ms	(cbrt (* (+ N 1.0) N))

simplify98.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	222	872
1	683	844
2	2971	788
3	5001	776

prune393.0ms

Filtered

104 candidates to 84 candidates (80.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	105	7	112

Merged error: 0.5b

Counts

112 → 7

regimes38.0ms

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

sample754.0ms

Algorithm

intervals

Results

406.0ms	2794×	body	1280	valid
131.0ms	4113×	body	80	valid
71.0ms	615×	body	640	valid
28.0ms	319×	body	320	valid
10.0ms	159×	body	160	valid