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

simplify6.0ms

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 (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))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 38

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
4.0ms	(- (atan (+ N 1.0)) (atan N))

series16.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
15.0ms	(- (atan (+ N 1.0)) (atan N))

simplify53.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (48.0ms)

Iter	Nodes	Cost
0	128	365
1	330	264
2	1376	254
3	5001	198

prune56.0ms

Filtered

44 candidates to 27 candidates (38.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	43	1	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	1	45

Merged error: 0.4b

Counts

45 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

1 → 9

Calls

1 calls:

1.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

series2.0ms

Counts

1 → 3

Calls

1 calls:

2.0ms

(atan2 1.0 (fma N (+ N 1.0) 1))

simplify108.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	21	57
1	32	50
2	55	50
3	70	50
4	89	50
5	143	50
6	567	50
7	1785	50
8	5001	50

prune23.0ms

Filtered

12 candidates to 9 candidates (25.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	10	2	12
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	10	3	13

Merged error: 0.4b

Counts

13 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.4b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.7b	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
13.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
13.9b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 90

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
6.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
1.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
2.0ms	(* (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))) (sqrt (atan2 1.0 (fma N (+ N 1.0) 1))))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify122.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (112.0ms)

Iter	Nodes	Cost
0	100	554
1	375	496
2	2224	476
3	5001	461

prune131.0ms

Filtered

102 candidates to 55 candidates (46.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	101	4	105

Merged error: 0.4b

Counts

105 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

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

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` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 50

Calls

4 calls:

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

series250.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
115.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
120.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify66.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	52	352
1	109	319
2	235	315
3	790	315
4	5001	315

prune146.0ms

Filtered

62 candidates to 46 candidates (25.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	61	1	62
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	61	5	66

Merged error: 0.4b

Counts

66 → 5

regimes22.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample759.0ms

Algorithm

intervals

Results

412.0ms	2876×	body	1280	valid
128.0ms	4046×	body	80	valid
70.0ms	616×	body	640	valid
28.0ms	311×	body	320	valid
10.0ms	151×	body	160	valid