Details

sample66.0ms

Algorithm

intervals

Results

24.0ms	50×	body	10240	exit
14.0ms	255×	body	80	valid
12.0ms	349×	body	80	nan
0.0ms	1×	body	160	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	315	5
5	1609	5
6	5001	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 0.1b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.1b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 48

Calls

3 calls:

5.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series89.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(pow (sqrt (atan2 b b)) (- b a))
56.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify46.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	148	324
1	412	298
2	1346	292
3	5001	290

prune99.0ms

Filtered

57 candidates to 36 candidates (63.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	55	2	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	2	58

Merged error: 0.1b

Counts

58 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`sqrt-prod`
14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`pow1` `unpow-prod-down`
6×	`sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `rem-sqrt-square`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
3.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series134.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
88.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
9.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify69.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	201	521
1	574	477
2	2332	466
3	5001	466

prune181.0ms

Filtered

78 candidates to 50 candidates (64.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	77	3	80

Merged error: 0.1b

Counts

80 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series42.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (atan2 b b))
9.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify96.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 7 (28.0ms)

Iter	Nodes	Cost
0	22	188
1	25	184
2	28	184
3	33	184
4	52	184
5	106	184
6	533	184
7	1765	180
8	5001	180

prune174.0ms

Filtered

64 candidates to 40 candidates (62.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	64	3	67

Merged error: 0.1b

Counts

67 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.1b	(sin (pow (atan2 b b) (* 1/2 (- b a))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`unpow-prod-up`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `add-cbrt-cube` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

3.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
3.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series80.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
61.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify57.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (53.0ms)

Iter	Nodes	Cost
0	145	236
1	453	212
2	1901	202
3	5001	199

prune52.0ms

Filtered

32 candidates to 21 candidates (65.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Merged error: 0.1b

Counts

35 → 3

regimes37.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	27
1	14	27

end0.0ms

sample2.0s

Algorithm

intervals

Results

771.0ms	1815×	body	10240	exit
457.0ms	7989×	body	80	valid
366.0ms	9961×	body	80	nan
3.0ms	1×	body	5120	valid
3.0ms	2×	body	2560	valid
1.0ms	2×	body	1280	valid
1.0ms	6×	body	160	valid

Details

sample66.0ms

simplify51.0ms

prune2.0ms

localize12.0ms

rewrite11.0ms

series89.0ms

simplify46.0ms

prune99.0ms

localize11.0ms

rewrite17.0ms

series134.0ms

simplify69.0ms

prune181.0ms

localize15.0ms

rewrite7.0ms

series42.0ms

simplify96.0ms

prune174.0ms

localize9.0ms

rewrite7.0ms

series80.0ms

simplify57.0ms

prune52.0ms

regimes37.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.0s

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