Details

sample26.0ms

Algorithm

intervals

Results

12.0ms	86×	body	1280	valid
4.0ms	142×	body	80	valid
2.0ms	15×	body	640	valid
1.0ms	7×	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 (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: 13.0b

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))

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))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	74	154
1	143	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune42.0ms

Filtered

28 candidates to 19 candidates (32.1%)

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)))

rewrite8.0ms

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)))

series49.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify54.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	120	152
1	432	127
2	2314	127
3	5002	127

prune48.0ms

Filtered

34 candidates to 22 candidates (35.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	2	34
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Merged error: 0.4b

Counts

35 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b	(* (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))))

rewrite12.0ms

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))))

series40.0ms

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)))))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
19.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify104.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	110	649
1	391	565
2	2228	539
3	5002	520

prune108.0ms

Filtered

94 candidates to 47 candidates (50.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	93	4	97

Merged error: 0.4b

Counts

97 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
13.9b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.2b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.2b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 42

Calls

4 calls:

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

series281.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
20.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
129.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
129.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify44.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 4 (39.0ms)

Iter	Nodes	Cost
0	63	394
1	99	347
2	245	337
3	795	336
4	5002	334

prune109.0ms

Filtered

54 candidates to 35 candidates (35.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	52	2	54
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	52	6	58

Merged error: 0.4b

Counts

58 → 6

regimes25.0ms

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

sample775.0ms

Algorithm

intervals

Results

413.0ms	2876×	body	1280	valid
142.0ms	4046×	body	80	valid
72.0ms	616×	body	640	valid
28.0ms	311×	body	320	valid
11.0ms	151×	body	160	valid