Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	85×	body	1280	valid
4.0ms	131×	body	80	valid
2.0ms	18×	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 (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: 14.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.4b	(- (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))

series13.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (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	2447	142
5	5001	142

prune45.0ms

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: 0.4b

Counts

29 → 2

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)))

series45.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify60.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (7.0ms)

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

prune64.0ms

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	1	0	1
Total	28	8	36

Merged error: 0.4b

Counts

36 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
15.4b	(cbrt (* (+ N 1.0) N))
15.4b	(cbrt (* (+ N 1.0) N))
15.4b	(cbrt (* (+ N 1.0) N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-div` `associate-*l/`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `flip3-+` `pow1/3` `flip-+`

Counts

4 → 40

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
4.0ms	(cbrt (* (+ N 1.0) N))
4.0ms	(cbrt (* (+ N 1.0) N))
5.0ms	(cbrt (* (+ N 1.0) N))

series309.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (* (cbrt (* (+ N 1.0) N)) (cbrt (* (+ N 1.0) N))) (cbrt (* (+ N 1.0) N)))))
101.0ms	(cbrt (* (+ N 1.0) N))
100.0ms	(cbrt (* (+ N 1.0) N))
101.0ms	(cbrt (* (+ N 1.0) N))

simplify74.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	208	572
1	609	524
2	2254	482
3	5001	474

prune161.0ms

Filtered

52 candidates to 47 candidates (90.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	53	7	60

Merged error: 0.4b

Counts

60 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow N 2) (+ (* 1.0 N) 1))
0.4b	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
4×	`*-un-lft-identity`
3×	`sum-log`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
1×	`+-commutative` `associate-+r+` `flip3-+` `flip-+` `distribute-lft-out`

Counts

2 → 21

Calls

2 calls:

7.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
1.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

series22.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(+ (pow N 2) (+ (* 1.0 N) 1))
3.0ms	(atan2 1.0 (+ (pow N 2) (+ (* 1.0 N) 1)))

simplify79.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (76.0ms)

Iter	Nodes	Cost
0	114	181
1	447	154
2	2686	153
3	5001	150

prune42.0ms

Filtered

27 candidates to 19 candidates (70.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	27	7	34

Merged error: 0.4b

Counts

34 → 7

regimes23.0ms

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	14	5
1	14	5

end0.0ms

sample767.0ms

Algorithm

intervals

Results

416.0ms	2860×	body	1280	valid
135.0ms	4043×	body	80	valid
75.0ms	639×	body	640	valid
28.0ms	300×	body	320	valid
11.0ms	158×	body	160	valid

Details

sample31.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite5.0ms

series13.0ms

simplify78.0ms

prune45.0ms

localize6.0ms

rewrite7.0ms

series45.0ms

simplify60.0ms

prune64.0ms

localize14.0ms

rewrite15.0ms

series309.0ms

simplify74.0ms

prune161.0ms

localize8.0ms

rewrite8.0ms

series22.0ms

simplify79.0ms

prune42.0ms

regimes23.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample767.0ms

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