Details

sample123.0ms

Algorithm

intervals

Results

65.0ms	63×	body	5120	exit
22.0ms	255×	body	80	valid
19.0ms	347×	body	80	nan
0.0ms	1×	body	320	valid

simplify54.0ms

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	321	5
5	1627	5
6	5001	5

prune3.0ms

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: 0.2b

Counts

2 → 1

localize8.0ms

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))

rewrite14.0ms

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

series93.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (sqrt (atan2 b b)) (- b a))
63.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
10.0ms	(sqrt (atan2 b b))

simplify77.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (71.0ms)

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

prune126.0ms

Filtered

72 candidates to 43 candidates (59.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	2	73

Merged error: 0.2b

Counts

73 → 2

localize13.0ms

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	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`cbrt-prod`
29×	`sqrt-prod`
19×	`add-cube-cbrt` `*-un-lft-identity`
14×	`pow1`
11×	`swap-sqr`
9×	`associate-r` `associate-l` `unswap-sqr`
6×	`add-exp-log` `pow1/3`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 103

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
8.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
10.0ms	(sqrt (atan2 b b))
110.0ms	(* (cbrt (sqrt (atan2 b b))) (cbrt (sqrt (atan2 b b))))

simplify121.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 4 (112.0ms)

Iter	Nodes	Cost
0	103	742
1	354	703
2	1192	651
3	3474	614
4	5001	598

prune235.0ms

Filtered

115 candidates to 67 candidates (58.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Merged error: 0.2b

Counts

117 → 2

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
14×	`add-cube-cbrt`
11×	`unpow-prod-up`
10×	`unpow-prod-down`
9×	`prod-diff`
7×	`log-pow`
6×	`pow1` `exp-prod` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 64

Calls

3 calls:

7.0ms	(pow (log (exp (sqrt (atan2 b b)))) (- b a))
6.0ms	(sin (pow (log (exp (sqrt (atan2 b b)))) (- b a)))
2.0ms	(sqrt (atan2 b b))

series92.0ms

Counts

3 → 9

Calls

3 calls:

19.0ms	(pow (log (exp (sqrt (atan2 b b)))) (- b a))
61.0ms	(sin (pow (log (exp (sqrt (atan2 b b)))) (- b a)))
11.0ms	(sqrt (atan2 b b))

simplify76.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	286	650
1	755	540
2	2683	523
3	5002	506

prune145.0ms

Filtered

73 candidates to 46 candidates (63.0%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	73	2	75

Merged error: 0.2b

Counts

75 → 2

regimes30.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	1704×	body	5120	exit
614.0ms	7987×	body	80	valid
551.0ms	9664×	body	80	nan
3.0ms	2×	body	2560	valid
2.0ms	4×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid

Details

sample123.0ms

simplify54.0ms

prune3.0ms

localize8.0ms

rewrite14.0ms

series93.0ms

simplify77.0ms

prune126.0ms

localize13.0ms

rewrite16.0ms

series140.0ms

simplify121.0ms

prune235.0ms

localize13.0ms

rewrite17.0ms

series92.0ms

simplify76.0ms

prune145.0ms

regimes30.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling