Details

analyze1.0ms

Algorithm

Search

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

sample27.0ms

Algorithm

intervals

Results

14.0ms	93×	body	1280	valid
4.0ms	129×	body	80	valid
2.0ms	17×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	7×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	70	7
1	70	7

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: 13.9b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(atan.f64 (+.f64 N 1))
2.1b	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

rewrite5.0ms

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))
4.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

series4.0ms

Counts

2 → 6

Calls

2 calls:

1.0ms	(atan.f64 (+.f64 N 1))
2.0ms	(-.f64 (atan.f64 (+.f64 N 1)) (atan.f64 N))

simplify63.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4923	236
1	4923	236

prune15.0ms

Filtered

19 candidates to 27 candidates (-42.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	25	2	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	25	3	28

Merged error: 0.7b

Counts

28 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(*.f64 N (+.f64 N 1))
0.7b	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

rewrite8.0ms

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))))

series7.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(*.f64 N (+.f64 N 1))
2.0ms	(atan2.f64 1 (+.f64 1 (*.f64 N (+.f64 N 1))))

simplify59.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5066	260

prune25.0ms

Filtered

26 candidates to 36 candidates (-38.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	33	3	36
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	34	5	39

Merged error: 0.7b

Counts

39 → 5

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 N N) N)
0.7b	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

rewrite8.0ms

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:

7.0ms	(+.f64 (*.f64 N N) N)
1.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

series7.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+.f64 (*.f64 N N) N)
2.0ms	(atan2.f64 1 (+.f64 1 (+.f64 (*.f64 N N) N)))

simplify70.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4939	216
1	4939	216

prune15.0ms

Filtered

19 candidates to 26 candidates (-36.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	26	5	31

Merged error: 0.7b

Counts

31 → 5

localize9.0ms

Local error

Found 4 expressions with local error:

0.7b	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))
17.0b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
17.0b	(cbrt.f64 (*.f64 N (+.f64 1 N)))
17.0b	(cbrt.f64 (*.f64 N (+.f64 1 N)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 40

Calls

4 calls:

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

series31.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(atan2.f64 1 (+.f64 1 (.f64 (.f64 (cbrt.f64 (.f64 N (+.f64 1 N))) (cbrt.f64 (.f64 N (+.f64 1 N)))) (cbrt.f64 (*.f64 N (+.f64 1 N))))))
10.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
8.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))
9.0ms	(cbrt.f64 (*.f64 N (+.f64 1 N)))

simplify43.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4899	568
1	4899	568

prune51.0ms

Filtered

50 candidates to 52 candidates (-4.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	52	5	57

Merged error: 0.7b

Counts

57 → 5

regimes37.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms

sample786.0ms

Algorithm

intervals

Results

420.0ms	2832×	body	1280	valid
137.0ms	4055×	body	80	valid
78.0ms	608×	body	640	valid
32.0ms	338×	body	320	valid
12.0ms	167×	body	160	valid

Details

analyze1.0ms

sample27.0ms

simplify7.0ms

prune1.0ms

localize6.0ms

rewrite5.0ms

series4.0ms

simplify63.0ms

prune15.0ms

localize8.0ms

rewrite8.0ms

series7.0ms

simplify59.0ms

prune25.0ms

localize5.0ms

rewrite8.0ms

series7.0ms

simplify70.0ms

prune15.0ms

localize9.0ms

rewrite17.0ms

series31.0ms

simplify43.0ms

prune51.0ms

regimes37.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample786.0ms

Profiling