Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	89×	body	1280	valid
5.0ms	18×	body	640	valid
4.0ms	122×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	8×	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 (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.5b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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:

0.0ms	(atan (+ N 1.0))
3.0ms	(- (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))

simplify50.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (45.0ms)

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

prune69.0ms

Filtered

44 candidates to 27 candidates (61.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ N 1.0) 1)
0.2b	(atan2 1.0 (fma N (+ N 1.0) 1))

rewrite1.0ms

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:

0.0ms	(fma N (+ N 1.0) 1)
0.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

series24.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(fma N (+ N 1.0) 1)
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

simplify133.0ms

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

prune52.0ms

Filtered

25 candidates to 19 candidates (76.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (* (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1))))
14.5b	(cbrt (fma N (+ N 1.0) 1))
14.5b	(cbrt (fma N (+ N 1.0) 1))
14.5b	(cbrt (fma N (+ N 1.0) 1))

rewrite2.0ms

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:

0.0ms	(atan2 1.0 (* (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1))))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))

series251.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (* (* (cbrt (fma N (+ N 1.0) 1)) (cbrt (fma N (+ N 1.0) 1))) (cbrt (fma N (+ N 1.0) 1))))
82.0ms	(cbrt (fma N (+ N 1.0) 1))
84.0ms	(cbrt (fma N (+ N 1.0) 1))
82.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify108.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (102.0ms)

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

prune171.0ms

Filtered

60 candidates to 50 candidates (83.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

13.9b	(sqrt (fma N (+ N 1.0) 1))
13.9b	(sqrt (fma N (+ N 1.0) 1))
14.5b	(cbrt (fma N (+ N 1.0) 1))
14.5b	(cbrt (fma N (+ N 1.0) 1))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

1.0ms	(sqrt (fma N (+ N 1.0) 1))
1.0ms	(sqrt (fma N (+ N 1.0) 1))
0.0ms	(cbrt (fma N (+ N 1.0) 1))
1.0ms	(cbrt (fma N (+ N 1.0) 1))

series243.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(sqrt (fma N (+ N 1.0) 1))
36.0ms	(sqrt (fma N (+ N 1.0) 1))
82.0ms	(cbrt (fma N (+ N 1.0) 1))
82.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify43.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (37.0ms)

Iter	Nodes	Cost
0	133	338
1	324	314
2	1036	310
3	5002	308

prune236.0ms

Filtered

68 candidates to 60 candidates (88.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.2b

regimes33.0ms

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	9	3
1	9	3

end0.0ms

sample717.0ms

Algorithm

intervals

Results

384.0ms	2911×	body	1280	valid
124.0ms	4026×	body	80	valid
63.0ms	590×	body	640	valid
26.0ms	310×	body	320	valid
13.0ms	163×	body	160	valid