Details

sample81.0ms

Algorithm

intervals

Results

24.0ms	45×	body	10240	exit
19.0ms	331×	body	80	nan
18.0ms	256×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1114
5	256
4	110
3	45
2	22
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.0b	(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` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series119.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
3	1729
2	682
1	308
0	117

prune412.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

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))

rewrite29.0ms

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×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
13.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series138.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
54.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
16.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
3	2010
2	761
1	338
0	122

prune756.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`unpow-prod-up`
18×	`prod-diff`
15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `unpow-prod-down` `add-exp-log`
2×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 48

Calls

2 calls:

21.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
6.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

series136.0ms

Counts

2 → 6

Calls

2 calls:

97.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
39.0ms	(pow (atan2 b b) (* 1/2 (- b a)))

simplify2.4s

Counts

54 → 54

Iterations

Iter	Nodes
done	5001
3	2765
2	787
1	354
0	144

prune198.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize51.0ms

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))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify3.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
9	1204
8	368
7	158
6	89
5	59
4	40
3	32
2	28
1	25
0	20

prune521.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes109.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	9
1	9
0	8

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.1s	1746×	body	10240	exit
1.4s	7986×	body	80	valid
1.0s	9649×	body	80	nan
6.0ms	1×	body	5120	valid
3.0ms	4×	body	640	valid
2.0ms	4×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	4×	body	160	valid