Details

sample28.0ms

Algorithm

intervals

Results

14.0ms	102×	body	1280	valid
4.0ms	131×	body	80	valid
2.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	5×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

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))
7.0ms	(- (atan (+ N 1.0)) (atan N))

series11.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify50.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (46.0ms)

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

prune73.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize6.0ms

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))

series19.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(fma N (+ N 1.0) 1)
2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

simplify140.0ms

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

prune53.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

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))))
17.6b	(cbrt (fma N (+ N 1.0) 1))
17.6b	(cbrt (fma N (+ N 1.0) 1))
17.6b	(cbrt (fma N (+ N 1.0) 1))

rewrite4.0ms

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))))
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))

series243.0ms

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))))
81.0ms	(cbrt (fma N (+ N 1.0) 1))
81.0ms	(cbrt (fma N (+ N 1.0) 1))
79.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify114.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 4 (109.0ms)

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

prune169.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

17.1b	(sqrt (fma N (+ N 1.0) 1))
17.1b	(sqrt (fma N (+ N 1.0) 1))
17.6b	(cbrt (fma N (+ N 1.0) 1))
17.6b	(cbrt (fma N (+ N 1.0) 1))

rewrite5.0ms

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

series238.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(sqrt (fma N (+ N 1.0) 1))
35.0ms	(sqrt (fma N (+ N 1.0) 1))
83.0ms	(cbrt (fma N (+ N 1.0) 1))
85.0ms	(cbrt (fma N (+ N 1.0) 1))

simplify50.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (39.0ms)

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

prune235.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b 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

sample762.0ms

Algorithm

intervals

Results

384.0ms	2852×	body	1280	valid
125.0ms	4071×	body	80	valid
76.0ms	595×	body	640	valid
27.0ms	306×	body	320	valid
11.0ms	176×	body	160	valid