Details

sample32.0ms

Algorithm

intervals

Results

16.0ms	105×	body	1280	valid
4.0ms	112×	body	80	valid
3.0ms	23×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	5×	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 (100.0%)

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: 17.7b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.2b	(- (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))

series3.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

simplify74.0ms

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	2447	142
5	5001	142

prune36.0ms

Filtered

28 candidates to 19 candidates (32.1%)

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: 0.1b

Counts

29 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.1b	(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)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(* (+ 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 (35.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	29	7	36

Merged error: 0.1b

Counts

36 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
16.5b	(cbrt (* (+ N 1.0) N))
16.5b	(cbrt (* (+ N 1.0) N))
16.5b	(cbrt (* (+ N 1.0) N))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

6.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))

series38.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
9.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))
10.0ms	(cbrt (* (+ N 1.0) N))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	362	890
1	1236	832
2	5001	754

prune220.0ms

Filtered

84 candidates to 67 candidates (20.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	84	7	91

Merged error: 0.1b

Counts

91 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
0.6b	(cbrt N)
16.5b	(cbrt (* (+ N 1.0) N))
16.5b	(cbrt (* (+ N 1.0) N))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

6.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
1.0ms	(cbrt N)
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))

series50.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N)))
21.0ms	(cbrt N)
9.0ms	(cbrt (* (+ N 1.0) N))
9.0ms	(cbrt (* (+ N 1.0) N))

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	399	785
1	1305	730
2	5002	647

prune191.0ms

Filtered

84 candidates to 64 candidates (23.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	84	7	91

Merged error: 0.1b

Counts

91 → 7

regimes85.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample860.0ms

Algorithm

intervals

Results

444.0ms	2845×	body	1280	valid
141.0ms	4054×	body	80	valid
86.0ms	647×	body	640	valid
28.0ms	291×	body	320	valid
12.0ms	163×	body	160	valid

Details

sample32.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series3.0ms

simplify74.0ms

prune36.0ms

localize6.0ms

rewrite7.0ms

series7.0ms

simplify56.0ms

prune57.0ms

localize12.0ms

rewrite21.0ms

series38.0ms

simplify43.0ms

prune220.0ms

localize16.0ms

rewrite18.0ms

series50.0ms

simplify43.0ms

prune191.0ms

regimes85.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample860.0ms

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