Details

sample27.0ms

Algorithm

intervals

Results

13.0ms	92×	body	1280	valid
5.0ms	138×	body	80	valid
1.0ms	13×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	3×	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: 12.7b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 15

Calls

1 calls:

3.0ms

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

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

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

simplify75.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 3 (11.0ms)

Iter	Nodes	Cost
0	72	123
1	142	114
2	286	112
3	678	111
4	2488	111
5	5001	111

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 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)))

rewrite8.0ms

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)))

series49.0ms

Counts

2 → 6

Calls

2 calls:

47.0ms	(* (+ 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

prune62.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1/3`

Counts

4 → 40

Calls

4 calls:

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

series379.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(atan2 1.0 (+ 1 (* (+ N 1.0) N)))
127.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
122.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
127.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify198.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 4 (32.0ms)

Iter	Nodes	Cost
0	51	407
1	72	353
2	192	341
3	656	341
4	3983	338
5	5001	338

prune287.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 4 expressions with local error:

15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
15.8b	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `pow1/3` `add-cbrt-cube` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

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

series486.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
120.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
123.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))
119.0ms	(cbrt (atan2 1.0 (+ 1 (* (+ N 1.0) N))))

simplify122.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (27.0ms)

Iter	Nodes	Cost
0	46	456
1	66	400
2	178	392
3	499	392
4	2312	388
5	5001	388

prune121.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.6b

regimes53.0ms

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	12	4
1	12	4

end0.0ms

sample785.0ms

Algorithm

intervals

Results

423.0ms	2886×	body	1280	valid
133.0ms	4013×	body	80	valid
79.0ms	620×	body	640	valid
29.0ms	317×	body	320	valid
11.0ms	164×	body	160	valid