Details

sample25.0ms

Algorithm

intervals

Results

10.0ms	78×	body	1280	valid
4.0ms	134×	body	80	valid
2.0ms	22×	body	640	valid
1.0ms	16×	body	320	valid
0.0ms	6×	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

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: 16.5b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.6b	(- (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))

series12.0ms

Counts

2 → 6

Calls

2 calls:

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

series48.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify56.0ms

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

prune57.0ms

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: 0.2b

Counts

36 → 8

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

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:

9.0ms	(* (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))

series387.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (cbrt (+ N 1.0)) (cbrt (+ N 1.0)))
92.0ms	(cbrt (+ N 1.0))
90.0ms	(cbrt (+ N 1.0))
91.0ms	(cbrt (+ N 1.0))

simplify148.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (138.0ms)

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

prune241.0ms

Filtered

107 candidates to 75 candidates (70.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	108	7	115

Merged error: 0.2b

Counts

115 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

26×	`cbrt-div`
13×	`cbrt-prod` `*-un-lft-identity`
9×	`flip3-+` `flip-+`
7×	`add-sqr-sqrt` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`distribute-lft-out`
2×	`associate-r/` `associate-l/`

Counts

4 → 59

Calls

4 calls:

3.0ms	(cbrt (+ N 1.0))
3.0ms	(cbrt (+ N 1.0))
7.0ms	(cbrt (+ N 1.0))
8.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))

series397.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(cbrt (+ N 1.0))
95.0ms	(cbrt (+ N 1.0))
96.0ms	(cbrt (+ N 1.0))
110.0ms	(cbrt (* (cbrt (+ N 1.0)) (cbrt (+ N 1.0))))

simplify80.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	296	612
1	778	576
2	2530	564
3	5002	564

prune239.0ms

Filtered

71 candidates to 61 candidates (85.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	71	7	78

Merged error: 0.2b

Counts

78 → 7

regimes51.0ms

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

sample748.0ms

Algorithm

intervals

Results

399.0ms	2845×	body	1280	valid
131.0ms	4047×	body	80	valid
73.0ms	651×	body	640	valid
28.0ms	311×	body	320	valid
9.0ms	146×	body	160	valid