Details

sample164.0ms

Algorithm

intervals

Results

32.0ms	47×	body	10240	exit
20.0ms	294×	body	80	nan
19.0ms	256×	body	80	valid

simplify797.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	444
4	117
3	45
2	22
1	13
0	7

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

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))

rewrite38.0ms

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:

22.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series166.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
30.0ms	(pow (sqrt (atan2 b b)) (- b a))
33.0ms	(sqrt (atan2 b b))

simplify834.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1098
1	315
0	117

prune326.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* 1 (pow (sqrt (atan2 b b)) (- b a))))
0.0b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite37.0ms

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:

20.0ms	(sin (* 1 (pow (sqrt (atan2 b b)) (- b a))))
13.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series119.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(sin (* 1 (pow (sqrt (atan2 b b)) (- b a))))
29.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1209
1	321
0	119

prune343.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
68.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series150.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
65.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
16.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

218 → 218

Iterations

Iter	Nodes
done	5001
2	3285
1	596
0	213

prune986.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* (+ (- a) a) 2))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`sqrt-prod`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

3 → 39

Calls

3 calls:

46.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* (+ (- a) a) 2))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series176.0ms

Counts

3 → 9

Calls

3 calls:

140.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (* 2 (- b a))) (pow (sqrt (sqrt (atan2 b b))) (* (+ (- a) a) 2))))
13.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify874.0ms

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
3	1092
2	276
1	103
0	56

prune295.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes116.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	15

end0.0ms

sample5.7s

Algorithm

intervals

Results

1.7s	7989×	body	80	valid
1.7s	1833×	body	10240	exit
1.5s	9748×	body	80	nan
6.0ms	3×	body	2560	valid
2.0ms	3×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	640	valid