Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	99×	body	1280	valid
4.0ms	124×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	8×	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: 13.8b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan (+ N 1.0))
1.6b	(- (atan (+ N 1.0)) (atan N))

rewrite5.0ms

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:

1.0ms	(atan (+ N 1.0))
3.0ms	(- (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))

simplify74.0ms

Algorithm

egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 3 (10.0ms)

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

prune51.0ms

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	(* (+ N 1.0) N)
0.2b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite10.0ms

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:

6.0ms	(* (+ N 1.0) N)
1.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series43.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 1 (4.0ms)

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

prune60.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt N) (cbrt N))
0.6b	(cbrt N)
0.6b	(cbrt N)
0.6b	(cbrt N)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* (cbrt N) (cbrt N))
1.0ms	(cbrt N)
1.0ms	(cbrt N)
4.0ms	(cbrt N)

series726.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(* (cbrt N) (cbrt N))
183.0ms	(cbrt N)
175.0ms	(cbrt N)
173.0ms	(cbrt N)

simplify88.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	115	288
1	472	261
2	2959	238
3	5003	235

prune209.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
0.2b	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
0.6b	(cbrt N)
29.7b	(cbrt (pow N 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

14×	`cbrt-prod`
9×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-cbrt-cube`
4×	`associate-*l/` `add-log-exp`
3×	`unpow-prod-down` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`pow1/3`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `unpow2` `sqr-pow`

Counts

4 → 57

Calls

4 calls:

1.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
10.0ms	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
1.0ms	(cbrt N)
2.0ms	(cbrt (pow N 2))

series425.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(atan2 1.0 (+ 1 (* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))))
64.0ms	(* (* (+ N 1.0) (cbrt (pow N 2))) (cbrt N))
175.0ms	(cbrt N)
180.0ms	(cbrt (pow N 2))

simplify39.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	265	414
1	1095	359
2	5002	342

prune181.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes28.0ms

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

sample727.0ms

Algorithm

intervals

Results

394.0ms	2829×	body	1280	valid
122.0ms	4035×	body	80	valid
71.0ms	649×	body	640	valid
27.0ms	315×	body	320	valid
11.0ms	172×	body	160	valid