Details

sample27.0ms

Algorithm

intervals

Results

14.0ms	97×	body	1280	valid
4.0ms	128×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	9×	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: 14.3b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
2.6b	(- (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:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 3 (47.0ms)

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

prune72.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ N 1.0) 1)
0.7b	(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))

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))

simplify142.0ms

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

prune57.0ms

Pruning

5 alts after pruning (4 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))
15.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
15.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite3.0ms

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:

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

series25.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify180.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 6 (45.0ms)

Iter	Nodes	Cost
0	37	296
1	62	276
2	100	276
3	148	276
4	341	276
5	975	276
6	3911	274
7	5001	274

prune134.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (fma N (+ N 1.0) 1))
15.6b	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.1b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
16.1b	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

rewrite3.0ms

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:

0.0ms	(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)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))
11.0ms	(sqrt (atan2 1.0 (fma N (+ N 1.0) 1)))
110.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))
107.0ms	(cbrt (atan2 1.0 (fma N (+ N 1.0) 1)))

simplify55.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	52	352
1	109	319
2	235	315
3	808	315
4	5002	315

prune177.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes19.0ms

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

sample766.0ms

Algorithm

intervals

Results

417.0ms	2952×	body	1280	valid
126.0ms	3956×	body	80	valid
73.0ms	638×	body	640	valid
26.0ms	297×	body	320	valid
10.0ms	157×	body	160	valid