Details

sample320.0ms

Algorithm

intervals

Results

28.0ms	54×	body	10240	exit
14.0ms	255×	body	80	valid
12.0ms	338×	body	80	nan
3.0ms	1×	body	5120	valid

simplify61.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	321	5
5	1627	5
6	5001	5

prune4.0ms

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: 0.3b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `pow-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`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 → 63

Calls

3 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
5.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(sqrt (atan2 b b))

series115.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(pow (sqrt (atan2 b b)) (- b a))
60.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
34.0ms	(sqrt (atan2 b b))

simplify84.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (72.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2703	425
3	5001	408

prune155.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 0.2b

Counts

73 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.3b	(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))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 171

Calls

4 calls:

22.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
4.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series146.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
83.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
14.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify66.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	451	2193
1	1880	1915
2	5002	1883

prune427.0ms

Filtered

183 candidates to 96 candidates (52.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	181	2	183
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	183	3	186

Merged error: 0.2b

Counts

186 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

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

series333.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(cbrt (atan2 b b))
105.0ms	(cbrt (atan2 b b))
107.0ms	(cbrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify109.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 5 (105.0ms)

Iter	Nodes	Cost
0	39	234
1	74	218
2	154	212
3	521	212
4	2941	211
5	5002	210

prune303.0ms

Filtered

66 candidates to 48 candidates (72.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 0.2b

Counts

69 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
20×	`add-sqr-sqrt`
18×	`sqrt-prod`
17×	`add-cube-cbrt` `*-un-lft-identity`
11×	`unpow-prod-up`
9×	`unpow-prod-down` `prod-diff`
7×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `cbrt-div` `pow1/3` `pow-sub` `sqr-pow`

Counts

4 → 80

Calls

4 calls:

6.0ms	(cbrt (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series89.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(cbrt (pow (sqrt (sqrt (atan2 b b))) (- b a)))
10.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))

simplify69.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (61.0ms)

Iter	Nodes	Cost
0	275	677
1	619	596
2	2336	587
3	5002	562

prune310.0ms

Filtered

92 candidates to 57 candidates (62.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Merged error: 0.2b

Counts

95 → 3

regimes45.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	23
1	20	23

end0.0ms

sample2.0s

Algorithm

intervals

Results

818.0ms	1851×	body	10240	exit
453.0ms	7988×	body	80	valid
364.0ms	9918×	body	80	nan
3.0ms	1×	body	5120	valid
2.0ms	4×	body	640	valid
1.0ms	1×	body	2560	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	160	valid
0.0ms	1×	body	320	valid