Details

sample671.0ms

Algorithm

intervals

Results

206.0ms	64×	body	10240	exit
70.0ms	256×	body	80	valid
53.0ms	380×	body	80	nan

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	7	492
1	13	492
2	22	492
3	45	492
4	110	492
5	256	492
6	1114	492
done	5001	492

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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:

7.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(sqrt (atan2 b b))

series139.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(pow (sqrt (atan2 b b)) (- b a))
78.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
27.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

72 → 72

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	117	39662
1	307	37381
2	677	35659
3	1701	35629
done	5001	35099

prune434.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 2 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `pow1` `unpow-prod-down` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-unpow` `pow-pow` `pow-exp` `sqr-pow`

Counts

2 → 26

Calls

2 calls:

3.0ms	(pow (atan2 b b) (* (- b a) 1/2))
12.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

series121.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(pow (atan2 b b) (* (- b a) 1/2))
79.0ms	(sin (pow (atan2 b b) (* (- b a) 1/2)))

simplify4.5s

Counts

32 → 32

Iterations

Useful iterations: 4 (2.8s)

Iter	Nodes	Cost
0	61	17363
1	139	16752
2	337	16202
3	1064	16067
4	3925	15987
done	5022	15987

prune183.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- b a) (log (atan2 b b)))
1.6b	(log (atan2 b b))
1.6b	(log (atan2 b b))
1.6b	(log (atan2 b b))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `log-prod`
13×	`*-un-lft-identity`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`add-exp-log`
6×	`add-cbrt-cube`
5×	`associate-l`
4×	`expm1-log1p-u` `associate-r` `log-pow` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `rem-log-exp`
2×	`associate-*l/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 73

Calls

4 calls:

25.0ms	(* (- b a) (log (atan2 b b)))
2.0ms	(log (atan2 b b))
2.0ms	(log (atan2 b b))
2.0ms	(log (atan2 b b))

series310.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* (- b a) (log (atan2 b b)))
73.0ms	(log (atan2 b b))
90.0ms	(log (atan2 b b))
82.0ms	(log (atan2 b b))

simplify2.7s

Counts

85 → 85

Iterations

Useful iterations: 3 (619.0ms)

Iter	Nodes	Cost
0	70	28072
1	143	26889
2	386	26605
3	1507	26525
done	5000	26525

prune535.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes97.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	493
1	9	493
done	9	493

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.8s	1909×	body	10240	exit
1.6s	9995×	body	80	nan
1.4s	7992×	body	80	valid
3.0ms	4×	body	640	valid
1.0ms	4×	body	160	valid