Details

sample336.0ms

Algorithm

intervals

Results

63.0ms	336×	body	80	nan
59.0ms	59×	body	10240	exit
27.0ms	256×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
7	2494
6	745
5	254
4	110
3	45
2	22
1	13
0	7

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 3 expressions with local error:

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

rewrite34.0ms

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	(pow (sqrt (atan2 b b)) (- b a))
16.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series183.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(pow (sqrt (atan2 b b)) (- b a))
113.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

72 → 72

Iterations

Iter	Nodes
4	3730
3	1582
2	623
1	296
0	117

prune703.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

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

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

34×	`sqrt-pow1`
30×	`pow1`
22×	`pow-pow`
18×	`pow1/2`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff` `pow-prod-up`
7×	`add-exp-log`
6×	`sqrt-prod`
5×	`pow-unpow` `pow-prod-down` `pow-sqr`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow-exp`
1×	`pow2` `pow-to-exp` `sub-neg` `unpow-prod-down` `pow-plus` `sqrt-unprod` `prod-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 93

Calls

4 calls:

26.0ms	(pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a))
29.0ms	(sin (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series161.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a))
92.0ms	(sin (pow (* (sqrt (sqrt (atan2 b b))) (sqrt (sqrt (atan2 b b)))) (- b a)))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify6.7s

Counts

105 → 105

Iterations

Iter	Nodes
4	4742
3	1752
2	704
1	350
0	151

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
22×	`unpow-prod-up` `log-pow`
21×	`exp-prod`
18×	`prod-diff`
12×	`unpow-prod-down`
9×	`sqrt-prod`
8×	`pow1`
6×	`log-prod`
5×	`pow-unpow` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `sin-sum`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `rem-log-exp` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 101

Calls

4 calls:

4.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
7.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
1.0ms	(sqrt (atan2 b b))

series163.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(pow (sqrt (atan2 b b)) (- b a))
85.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
31.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
12.0ms	(sqrt (atan2 b b))

simplify1.7s

Counts

113 → 113

Iterations

Iter	Nodes
4	3321
3	1431
2	639
1	355
0	188

prune1.4s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes76.0ms

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
1	9
0	9

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.0s	1854×	body	10240	exit
1.7s	7988×	body	80	valid
1.7s	9776×	body	80	nan
8.0ms	1×	body	5120	valid
4.0ms	2×	body	2560	valid
3.0ms	2×	body	1280	valid
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	640	valid