Details

sample320.0ms

Algorithm

intervals

Results

23.0ms	50×	body	10240	exit
15.0ms	256×	body	80	valid
12.0ms	282×	body	80	nan

simplify59.0ms

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

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: 0.0b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`unpow-prod-down` `sqrt-prod`
5×	`pow1` `pow-unpow`
3×	`add-exp-log` `pow-pow`
2×	`expm1-log1p-u` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

2 → 54

Calls

2 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
4.0ms	(sqrt (atan2 b b))

series56.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(pow (sqrt (atan2 b b)) (- b a))
33.0ms	(sqrt (atan2 b b))

simplify66.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	224	417
1	632	348
2	2275	345
3	5001	329

prune124.0ms

Filtered

60 candidates to 33 candidates (55.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	1	61

Merged error: 0b

Counts

61 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

10.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
7.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series78.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
29.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
10.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify91.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 3 (77.0ms)

Iter	Nodes	Cost
0	264	1026
1	731	882
2	2885	870
3	5002	838

prune313.0ms

Filtered

130 candidates to 72 candidates (55.4%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	130	1	131

Merged error: 0b

Counts

131 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12

end0.0ms

sample2.0s

Algorithm

intervals

Results

811.0ms	1850×	body	10240	exit
468.0ms	7992×	body	80	valid
381.0ms	9893×	body	80	nan
5.0ms	2×	body	5120	valid
3.0ms	2×	body	2560	valid
1.0ms	2×	body	640	valid
0.0ms	2×	body	160	valid