Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample32.0ms

Algorithm

intervals

Results

17.0ms	114×	body	1280	valid
4.0ms	109×	body	80	valid
3.0ms	24×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.5b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

0.9b	(- (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 → 14

Calls

1 calls:

3.0ms

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

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

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

simplify66.0ms

Algorithm

egg-herbie

Counts

17 → 17

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5339	182

prune31.0ms

Filtered

12 candidates to 17 candidates (-41.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	15	2	17
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	16	2	18

Merged error: 0.3b

Counts

18 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(* N (+ N 1.0))
0.3b	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

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

series7.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(* N (+ N 1.0))
2.0ms	(atan2 1.0 (+ 1 (* N (+ N 1.0))))

simplify60.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4907	272
1	4907	272

prune64.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	30	6	36
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	31	7	38

Merged error: 0.3b

Counts

38 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.0ms

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:

1.0ms	(cbrt N)
1.0ms	(cbrt N)
1.0ms	(cbrt N)
5.0ms	(* (cbrt N) (cbrt N))

series92.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt N)
22.0ms	(cbrt N)
21.0ms	(cbrt N)
27.0ms	(* (cbrt N) (cbrt N))

simplify45.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5165	356

prune102.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	85	7	92

Merged error: 0.3b

Counts

92 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (* N N)) (* (+ 1.0 N) (cbrt N)))
0.3b	(atan2 1.0 (+ 1 (* (cbrt (* N N)) (* (+ 1.0 N) (cbrt N)))))
0.5b	(cbrt N)
34.3b	(cbrt (* N N))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 48

Calls

4 calls:

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

series53.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (cbrt (* N N)) (* (+ 1.0 N) (cbrt N)))
3.0ms	(atan2 1.0 (+ 1 (* (cbrt (* N N)) (* (+ 1.0 N) (cbrt N)))))
21.0ms	(cbrt N)
21.0ms	(cbrt (* N N))

simplify39.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4913	367
1	4913	367

prune69.0ms

Filtered

44 candidates to 60 candidates (-36.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	60	7	67

Merged error: 0.3b

Counts

67 → 7

regimes42.0ms

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	11	9
1	11	9

end0.0ms

sample803.0ms

Algorithm

intervals

Results

439.0ms	2886×	body	1280	valid
142.0ms	4022×	body	80	valid
81.0ms	652×	body	640	valid
30.0ms	286×	body	320	valid
11.0ms	154×	body	160	valid

Details

analyze1.0ms

sample32.0ms

simplify5.0ms

prune2.0ms

localize6.0ms

rewrite4.0ms

series3.0ms

simplify66.0ms

prune31.0ms

localize6.0ms

rewrite7.0ms

series7.0ms

simplify60.0ms

prune64.0ms

localize9.0ms

rewrite10.0ms

series92.0ms

simplify45.0ms

prune102.0ms

localize10.0ms

rewrite15.0ms

series53.0ms

simplify39.0ms

prune69.0ms

regimes42.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample803.0ms

Profiling