Details

sample26.0ms

Algorithm

intervals

Results

13.0ms	98×	body	1280	valid
4.0ms	130×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	3×	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

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
0.8b	(- (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))

series12.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
11.0ms	(- (atan (+ N 1.0)) (atan N))

simplify47.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	129	365
1	345	264
2	1480	254
3	5001	198

prune72.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize5.0ms

Local error

Found 2 expressions with local error:

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

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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`
1×	`fma-udef`

Counts

2 → 19

Calls

2 calls:

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

series21.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(fma N (+ N 1.0) 1)
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

simplify141.0ms

Algorithm

egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	101
1	104	89
2	513	89
3	4531	89
4	5001	89

prune58.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(atan2 1.0 (* (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1))))
18.2b	(cbrt (fma N (+ N 1.0) 1))
18.2b	(cbrt (fma N (+ N 1.0) 1))
18.2b	(cbrt (fma N (+ N 1.0) 1))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

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

series457.0ms

Counts

4 → 12

Calls

4 calls:

199.0ms	(atan2 1.0 (* (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1))))
86.0ms	(cbrt (fma N (+ N 1.0) 1))
86.0ms	(cbrt (fma N (+ N 1.0) 1))
86.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify114.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (108.0ms)

Iter	Nodes	Cost
0	102	450
1	231	398
2	651	392
3	2666	383
4	5001	377

prune177.0ms

Filtered

60 candidates to 50 candidates (83.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

18.2b	(cbrt (fma N (+ N 1.0) 1))
18.2b	(cbrt (fma N (+ N 1.0) 1))
18.2b	(cbrt (fma N (+ N 1.0) 1))
18.2b	(cbrt (fma N (+ N 1.0) 1))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

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

series334.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(cbrt (fma N (+ N 1.0) 1))
83.0ms	(cbrt (fma N (+ N 1.0) 1))
83.0ms	(cbrt (fma N (+ N 1.0) 1))
84.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify120.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 4 (114.0ms)

Iter	Nodes	Cost
0	90	380
1	218	344
2	636	336
3	2640	336
4	5001	328

prune220.0ms

Filtered

64 candidates to 56 candidates (87.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

regimes24.0ms

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	9	3
1	9	3

end0.0ms

sample725.0ms

Algorithm

intervals

Results

395.0ms	2891×	body	1280	valid
123.0ms	4053×	body	80	valid
73.0ms	620×	body	640	valid
24.0ms	283×	body	320	valid
10.0ms	153×	body	160	valid