Details

sample27.0ms

Algorithm

intervals

Results

14.0ms	92×	body	1280	valid
4.0ms	138×	body	80	valid
1.0ms	13×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	3×	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: 12.7b

localize6.0ms

Local error

Found 1 expressions with local error:

1.3b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 29

Calls

1 calls:

4.0ms

(- (atan (+ N 1.0)) (atan N))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(- (atan (+ N 1.0)) (atan N))

simplify49.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (45.0ms)

Iter	Nodes	Cost
0	126	328
1	342	227
2	1471	217
3	5001	161

prune51.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.7b

localize6.0ms

Local error

Found 1 expressions with local error:

0.7b	(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))

simplify97.0ms

Algorithm

egg-herbie

Counts

12 → 12

Iterations

Useful iterations: 1 (3.0ms)

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	1779	50
8	5001	50

prune30.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (fma N (+ N 1.0) 1))
0.7b	(atan2 1.0 (fma N (+ N 1.0) 1))
15.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `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`

Counts

4 → 48

Calls

4 calls:

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

series27.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify102.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 6 (33.0ms)

Iter	Nodes	Cost
0	37	296
1	62	276
2	100	276
3	148	276
4	283	276
5	830	276
6	2927	274
7	5002	274

prune130.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (fma N (+ N 1.0) 1))
15.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.2b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
12.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify177.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 6 (44.0ms)

Iter	Nodes	Cost
0	37	330
1	62	314
2	100	314
3	148	314
4	341	314
5	975	314
6	3911	311
7	5001	311

prune161.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.6b

regimes25.0ms

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

sample707.0ms

Algorithm

intervals

Results

381.0ms	2886×	body	1280	valid
116.0ms	4013×	body	80	valid
71.0ms	620×	body	640	valid
27.0ms	317×	body	320	valid
13.0ms	164×	body	160	valid