Details

sample29.0ms

Algorithm

intervals

Results

13.0ms	83×	body	1280	valid
5.0ms	138×	body	80	valid
3.0ms	22×	body	640	valid
1.0ms	9×	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

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: 14.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

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

simplify78.0ms

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 (2 fresh and 0 done)

	Pruned	Kept	Total
New	26	2	28
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	2	29

Merged error: 0.6b

Counts

29 → 2

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)))

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)))

series47.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(* (+ N 1.0) N)
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify55.0ms

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

prune53.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	30	4	34
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	30	6	36

Merged error: 0.6b

Counts

36 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

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:

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

series533.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify89.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (84.0ms)

Iter	Nodes	Cost
0	75	232
1	164	204
2	533	198
3	2411	194
4	5001	191

prune118.0ms

Filtered

52 candidates to 44 candidates (84.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	51	7	58

Merged error: 0.6b

Counts

58 → 7

localize8.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.6b	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))))
13.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
13.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 82

Calls

4 calls:

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

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
3.0ms	(* (sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N)))) (sqrt (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))))

simplify111.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	110	649
1	391	565
2	2248	539
3	5001	520

prune113.0ms

Filtered

94 candidates to 47 candidates (50.0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Merged error: 0.5b

Counts

101 → 8

regimes31.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.4b 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

sample794.0ms

Algorithm

intervals

Results

437.0ms	2872×	body	1280	valid
135.0ms	4072×	body	80	valid
73.0ms	594×	body	640	valid
33.0ms	315×	body	320	valid
10.0ms	147×	body	160	valid