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

simplify5.0ms

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))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-atan` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 22

Calls

2 calls:

0.0ms	(atan (+ N 1.0))
2.0ms	(- (atan (+ N 1.0)) (atan N))

series13.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan (+ N 1.0))
12.0ms	(- (atan (+ N 1.0)) (atan N))

simplify75.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	75	154
1	145	145
2	289	143
3	681	142
4	2491	142
5	5001	142

prune53.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* (+ N 1.0) N)
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
3×	`associate-r`
2×	`associate-*l/` `add-log-exp`
1×	`flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `unswap-sqr`

Counts

2 → 28

Calls

2 calls:

13.0ms	(* (+ N 1.0) N)
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series44.0ms

Counts

2 → 6

Calls

2 calls:

41.0ms	(* (+ N 1.0) N)
3.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify57.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	121	151
1	432	127
2	2321	127
3	5002	127

prune66.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.6b	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
0.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
1.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

series34.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify73.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (8.0ms)

Iter	Nodes	Cost
0	49	332
1	79	294
2	159	294
3	330	292
4	1202	292
5	5002	292

prune106.0ms

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

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` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 42

Calls

4 calls:

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

series263.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
14.0ms	(sqrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
121.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
125.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify46.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 4 (41.0ms)

Iter	Nodes	Cost
0	63	394
1	99	347
2	248	337
3	864	336
4	5001	334

prune131.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.6b

regimes23.0ms

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	12	4
1	12	4

end0.0ms

sample765.0ms

Algorithm

intervals

Results

424.0ms	2952×	body	1280	valid
126.0ms	3956×	body	80	valid
74.0ms	638×	body	640	valid
26.0ms	297×	body	320	valid
11.0ms	157×	body	160	valid