Details

sample72.0ms

Algorithm

intervals

Results

23.0ms	61×	body	10240	exit
15.0ms	348×	body	80	nan
14.0ms	256×	body	80	valid

simplify51.0ms

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
done	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

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))

rewrite29.0ms

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` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

13.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series100.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(pow (sqrt (atan2 b b)) (- b a))
62.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
12.0ms	(sqrt (atan2 b b))

simplify74.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2703	425
3	5001	408
done	5001	408

prune156.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
0.0b	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-exp-log` `add-sqr-sqrt`
16×	`pow-exp`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff` `prod-exp`
7×	`pow1` `pow-to-exp`
6×	`sqrt-prod`
5×	`pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `unpow1/2`
1×	`pow2` `sub-neg` `unpow-prod-down` `sqrt-unprod` `pow-prod-down` `pow-sqr` `pow-prod-up` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 84

Calls

4 calls:

17.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
22.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series111.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a))
61.0ms	(sin (pow (* (pow (sqrt (atan2 b b)) 1/2) (pow (sqrt (atan2 b b)) 1/2)) (- b a)))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify139.0ms

Counts

96 → 96

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	276	831
1	750	629
2	3971	600
3	5001	598
done	5001	598

prune235.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
1.0b	(sqrt (atan2 b b))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

30.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
2.0ms	(sqrt (atan2 b b))

series100.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
11.0ms	(sqrt (atan2 b b))

simplify34.0ms

Counts

30 → 30

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	94	187
1	229	165
2	839	158
3	5001	155
done	5001	155

prune95.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a)))))
0.0b	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
0.0b	(expm1 (log1p (sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))))
1.0b	(sqrt (atan2 b b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 46

Calls

4 calls:

0.0ms	(log1p (sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a)))))
27.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
0.0ms	(expm1 (log1p (sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))))
1.0ms	(sqrt (atan2 b b))

series361.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(log1p (sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a)))))
88.0ms	(sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))
126.0ms	(expm1 (log1p (sin (pow (pow (sqrt (atan2 b b)) 1/2) (* 2 (- b a))))))
11.0ms	(sqrt (atan2 b b))

simplify47.0ms

Counts

58 → 58

Iterations

Useful iterations: 3 (42.0ms)

Iter	Nodes	Cost
0	144	491
1	345	427
2	1210	410
3	5002	392
done	5002	392

prune192.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes31.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	12	7
done	12	7

end0.0ms

sample2.3s

Algorithm

intervals

Results

775.0ms	1848×	body	10240	exit
594.0ms	9800×	body	80	nan
455.0ms	7991×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	2×	body	2560	valid
2.0ms	3×	body	1280	valid
1.0ms	2×	body	640	valid
0.0ms	1×	body	320	valid