Details

sample29.0ms

Algorithm

intervals

Results

15.0ms	109×	body	1280	valid
4.0ms	120×	body	80	valid
1.0ms	10×	body	640	valid
1.0ms	12×	body	320	valid
0.0ms	5×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.2b

localize6.0ms

Local error

Found 1 expressions with local error:

1.9b	(- (atan (+ N 1.0)) (atan N))

rewrite8.0ms

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:

7.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify46.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (43.0ms)

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: 0.6b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma N (+ N 1.0) 1)
0.6b	(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))

series25.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(fma N (+ N 1.0) 1)
5.0ms	(atan2 1.0 (fma N (+ N 1.0) 1))

simplify138.0ms

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

prune56.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (sqrt (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1)))
0.6b	(atan2 1.0 (* (sqrt (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1))))
18.3b	(sqrt (fma N (+ N 1.0) 1))
18.3b	(sqrt (fma N (+ N 1.0) 1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
24×	`sqrt-prod`
21×	`pow1`
14×	`add-cube-cbrt` `*-un-lft-identity`
10×	`sqrt-pow1` `pow1/2`
8×	`swap-sqr`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

14.0ms	(* (sqrt (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1)))
0.0ms	(atan2 1.0 (* (sqrt (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1))))
2.0ms	(sqrt (fma N (+ N 1.0) 1))
2.0ms	(sqrt (fma N (+ N 1.0) 1))

series101.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* (sqrt (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1)))
2.0ms	(atan2 1.0 (* (sqrt (fma N (+ N 1.0) 1)) (sqrt (fma N (+ N 1.0) 1))))
38.0ms	(sqrt (fma N (+ N 1.0) 1))
42.0ms	(sqrt (fma N (+ N 1.0) 1))

simplify160.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	152	528
1	551	459
2	3555	439
3	5001	439

prune195.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(atan2 1.0 (* (* (sqrt (sqrt (fma N (+ N 1.0) 1))) (sqrt (sqrt (fma N (+ N 1.0) 1)))) (sqrt (fma N (+ N 1.0) 1))))
18.3b	(sqrt (fma N (+ N 1.0) 1))
18.3b	(sqrt (fma N (+ N 1.0) 1))
18.3b	(sqrt (fma N (+ N 1.0) 1))

rewrite9.0ms

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:

3.0ms	(atan2 1.0 (* (* (sqrt (sqrt (fma N (+ N 1.0) 1))) (sqrt (sqrt (fma N (+ N 1.0) 1)))) (sqrt (fma N (+ N 1.0) 1))))
2.0ms	(sqrt (fma N (+ N 1.0) 1))
2.0ms	(sqrt (fma N (+ N 1.0) 1))
2.0ms	(sqrt (fma N (+ N 1.0) 1))

series121.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2 1.0 (* (* (sqrt (sqrt (fma N (+ N 1.0) 1))) (sqrt (sqrt (fma N (+ N 1.0) 1)))) (sqrt (fma N (+ N 1.0) 1))))
43.0ms	(sqrt (fma N (+ N 1.0) 1))
38.0ms	(sqrt (fma N (+ N 1.0) 1))
38.0ms	(sqrt (fma N (+ N 1.0) 1))

simplify84.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 4 (78.0ms)

Iter	Nodes	Cost
0	82	411
1	189	362
2	583	362
3	2230	359
4	5001	356

prune199.0ms

Pruning

6 alts after pruning (4 fresh and 2 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

sample752.0ms

Algorithm

intervals

Results

371.0ms	2851×	body	1280	valid
129.0ms	4049×	body	80	valid
66.0ms	614×	body	640	valid
30.0ms	328×	body	320	valid
10.0ms	158×	body	160	valid