Details

analyze2.0ms

Algorithm

Search

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

sample33.0ms

Algorithm

intervals

Results

15.0ms	72×	body	2048	valid
6.0ms	39×	body	1024	valid
4.0ms	111×	body	128	valid
2.0ms	23×	body	512	valid
1.0ms	11×	body	256	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune1.0ms

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: 18.6b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
1.6b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `diff-atan_binary64`

Counts

2 → 21

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
3.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series36.0ms

Counts

2 → 6

Calls

2 calls:

7.0ms	(atan.f64 (+.f64 N 1))
29.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify94.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4850	376
1	4850	376

prune20.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	26	2	28

Merged error: 0.4b

Counts

28 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.4b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`add-log-exp_binary64` `associate-*r/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

2 → 30

Calls

2 calls:

6.0ms	(*.f64 N (+.f64 N 1))
1.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

series67.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(*.f64 N (+.f64 N 1))
14.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify71.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5424	383

prune38.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	30	8	38

Merged error: 0.3b

Counts

38 → 8

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 N N) N)
0.4b	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
1×	`flip3-+_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

2 → 20

Calls

2 calls:

5.0ms	(+.f64 (*.f64 N N) N)
1.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

series67.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(+.f64 (*.f64 N N) N)
14.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

simplify65.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5057	318

prune23.0ms

Filtered

19 candidates to 26 candidates (-36.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	26	8	34

Merged error: 0.3b

Counts

34 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 N 1))
0.3b	(cbrt.f64 (+.f64 1 N))
0.3b	(cbrt.f64 (+.f64 1 N))
0.4b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 N 1)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
12×	`cbrt-prod_binary64`
7×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-div_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3-+_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`

Counts

4 → 49

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 N 1))
3.0ms	(cbrt.f64 (+.f64 1 N))
3.0ms	(cbrt.f64 (+.f64 1 N))
1.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 N 1)))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(cbrt.f64 (+.f64 N 1))
41.0ms	(cbrt.f64 (+.f64 1 N))
41.0ms	(cbrt.f64 (+.f64 1 N))
20.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 N (*.f64 (cbrt.f64 (+.f64 1 N)) (cbrt.f64 (+.f64 1 N)))) (cbrt.f64 (+.f64 N 1)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5102	810

prune69.0ms

Filtered

50 candidates to 61 candidates (-22.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	60	1	61
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	62	7	69

Merged error: 0.3b

Counts

69 → 7

regimes31.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	9	13

end0.0ms

sample961.0ms

Algorithm

intervals

Results

458.0ms	2183×	body	2048	valid
161.0ms	4011×	body	128	valid
157.0ms	1053×	body	1024	valid
59.0ms	515×	body	512	valid
18.0ms	238×	body	256	valid

Details

analyze2.0ms

sample33.0ms

simplify11.0ms

prune1.0ms

localize6.0ms

rewrite6.0ms

series36.0ms

simplify94.0ms

prune20.0ms

localize6.0ms

rewrite9.0ms

series67.0ms

simplify71.0ms

prune38.0ms

localize6.0ms

rewrite6.0ms

series67.0ms

simplify65.0ms

prune23.0ms

localize12.0ms

rewrite15.0ms

series142.0ms

simplify81.0ms

prune69.0ms

regimes31.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample961.0ms

Profiling