Details

sample25.0ms

Algorithm

intervals

Results

12.0ms	88×	body	1280	valid
4.0ms	134×	body	80	valid
2.0ms	20×	body	640	valid
1.0ms	8×	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: 14.1b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.5b	(- (atan (+ N 1.0)) (atan N))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

1×	`sub-neg` `flip3--` `diff-atan` `flip--`

Counts

2 → 5

Calls

2 calls:

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

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
10.0ms	(- (atan (+ N 1.0)) (atan N))

simplify54.0ms

Algorithm

egg-herbie

Counts

11 → 11

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	52	58
1	106	58
2	194	56
3	370	55
4	1482	55
5	5002	55

prune15.0ms

Filtered

11 candidates to 4 candidates (36.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	10	1	11
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	2	12

Merged error: 0.3b

Counts

12 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.3b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-*l/`
1×	`flip3-+` `*-commutative` `flip-+`

Counts

2 → 3

Calls

2 calls:

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

series43.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify201.0ms

Algorithm

egg-herbie

Counts

9 → 9

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	44	32
1	100	29
2	305	29
3	913	29
4	4006	29
5	5001	29

prune21.0ms

Filtered

9 candidates to 5 candidates (55.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	7	2	9
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	7	4	11

Merged error: 0.3b

Counts

11 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* N N) (* 1.0 1.0))
0.0b	(* (- (* N N) (* 1.0 1.0)) N)
0.3b	(atan2 1.0 (+ 1 (/ (* (- (* N N) (* 1.0 1.0)) N) (- N 1.0))))
4.7b	(/ (* (- (* N N) (* 1.0 1.0)) N) (- N 1.0))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-commutative`
12×	`difference-of-squares`
8×	`associate-l`
6×	`associate-/l*`
4×	`flip3--` `associate-*l/` `flip--`
2×	`associate-/r/` `associate-/l/`
1×	`sub-neg` `frac-2neg` `clear-num` `div-inv`

Counts

4 → 28

Calls

4 calls:

5.0ms	(- (* N N) (* 1.0 1.0))
6.0ms	(* (- (* N N) (* 1.0 1.0)) N)
1.0ms	(atan2 1.0 (+ 1 (/ (* (- (* N N) (* 1.0 1.0)) N) (- N 1.0))))
8.0ms	(/ (* (- (* N N) (* 1.0 1.0)) N) (- N 1.0))

series244.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* N N) (* 1.0 1.0))
76.0ms	(* (- (* N N) (* 1.0 1.0)) N)
5.0ms	(atan2 1.0 (+ 1 (/ (* (- (* N N) (* 1.0 1.0)) N) (- N 1.0))))
118.0ms	(/ (* (- (* N N) (* 1.0 1.0)) N) (- N 1.0))

simplify58.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 3 (54.0ms)

Iter	Nodes	Cost
0	176	179
1	549	160
2	2148	143
3	5001	140

prune69.0ms

Filtered

40 candidates to 23 candidates (57.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	37	3	40
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	39	5	44

Merged error: 0.3b

Counts

44 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ 1 N) (+ N 1.0))
0.1b	(/ 1 (/ (/ 1 N) (+ N 1.0)))
0.3b	(atan2 1.0 (+ 1 (/ 1 (/ (/ 1 N) (+ N 1.0)))))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

11×	`associate-/r/`
8×	`associate-/l/`
7×	`clear-num`
6×	`div-inv`
5×	`frac-2neg`
4×	`remove-double-div`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `flip-+`
1×	`inv-pow`

Counts

3 → 27

Calls

3 calls:

4.0ms	(/ (/ 1 N) (+ N 1.0))
5.0ms	(/ 1 (/ (/ 1 N) (+ N 1.0)))
1.0ms	(atan2 1.0 (+ 1 (/ 1 (/ (/ 1 N) (+ N 1.0)))))

series79.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(/ (/ 1 N) (+ N 1.0))
41.0ms	(/ 1 (/ (/ 1 N) (+ N 1.0)))
3.0ms	(atan2 1.0 (+ 1 (/ 1 (/ (/ 1 N) (+ N 1.0)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	118	101
1	463	93
2	2544	92
3	5002	92

prune56.0ms

Filtered

36 candidates to 23 candidates (63.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	36	0	36
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	36	5	41

Merged error: 0.3b

Counts

41 → 5

regimes40.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	4
1	12	4

end0.0ms

sample725.0ms

Algorithm

intervals

Results

394.0ms	2883×	body	1280	valid
126.0ms	4068×	body	80	valid
66.0ms	609×	body	640	valid
26.0ms	300×	body	320	valid
9.0ms	140×	body	160	valid