Details

sample30.0ms

Algorithm

intervals

Results

15.0ms	91×	body	1280	valid
5.0ms	131×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	3×	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: 15.2b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.6b	(- (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))

simplify77.0ms

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

prune46.0ms

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: 0.4b

Counts

29 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.4b	(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)))

series50.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(* (+ N 1.0) N)
3.0ms	(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

prune62.0ms

Filtered

34 candidates to 22 candidates (64.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	28	6	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	7	35

Merged error: 0.4b

Counts

35 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite11.0ms

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:

6.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)

series752.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(* (cbrt N) (cbrt N))
191.0ms	(cbrt N)
186.0ms	(cbrt N)
180.0ms	(cbrt N)

simplify94.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (82.0ms)

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

prune360.0ms

Filtered

85 candidates to 64 candidates (75.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Merged error: 0.4b

Counts

92 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
0.4b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
0.6b	(cbrt N)
28.2b	(cbrt (pow N 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
9×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-cbrt-cube`
4×	`associate-*l/` `add-log-exp`
3×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

10.0ms	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
1.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
1.0ms	(cbrt N)
2.0ms	(cbrt (pow N 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
6.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
166.0ms	(cbrt N)
173.0ms	(cbrt (pow N 2))

simplify45.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	265	414
1	1095	359
2	5002	342

prune159.0ms

Filtered

69 candidates to 52 candidates (75.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	2	3	5
Picked	0	1	1
Done	0	2	2
Total	70	7	77

Merged error: 0.4b

Counts

77 → 7

regimes25.0ms

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

sample819.0ms

Algorithm

intervals

Results

452.0ms	2918×	body	1280	valid
140.0ms	3955×	body	80	valid
79.0ms	632×	body	640	valid
33.0ms	339×	body	320	valid
11.0ms	156×	body	160	valid