Details

sample417.0ms

Algorithm

intervals

Results

37.0ms	348×	body	80	nan
28.0ms	61×	body	10240	exit
16.0ms	256×	body	80	valid

simplify56.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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))

rewrite26.0ms

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:

8.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
4.0ms	(sqrt (atan2 b b))

series118.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(pow (sqrt (atan2 b b)) (- b a))
75.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(sqrt (atan2 b b))

simplify74.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (68.0ms)

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

prune159.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (* 1/2 (- b a)))
0.0b	(sin (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` `add-cube-cbrt` `*-un-lft-identity`
11×	`distribute-rgt-in` `distribute-lft-in`
3×	`pow1` `add-exp-log` `unpow-prod-down`
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:

8.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
20.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

series87.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
62.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))

simplify100.0ms

Counts

54 → 54

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	324	582
1	913	448
2	3681	428
3	5001	425
done	5001	425

prune97.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
18.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0ms	(log1p (expm1 (sin (pow (atan2 b b) (* 1/2 (- b a))))))
1.0ms	(expm1 (sin (pow (atan2 b b) (* 1/2 (- b a)))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(pow (atan2 b b) (* 1/2 (- b a)))
65.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
103.0ms	(log1p (expm1 (sin (pow (atan2 b b) (* 1/2 (- b a))))))
102.0ms	(expm1 (sin (pow (atan2 b b) (* 1/2 (- b a)))))

simplify134.0ms

Counts

82 → 82

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	386	816
1	1112	648
2	4650	622
3	5001	622
done	5001	622

prune188.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

5×	`log1p-expm1-u`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
2×	`expm1-log1p` `expm1-udef`
1×	`log1p-udef` `log1p-expm1`

Counts

4 → 42

Calls

4 calls:

18.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
0.0ms	(log1p (expm1 (expm1 (log1p (sin (pow (atan2 b b) (* 1/2 (- b a))))))))
0.0ms	(expm1 (log1p (sin (pow (atan2 b b) (* 1/2 (- b a))))))
1.0ms	(expm1 (expm1 (log1p (sin (pow (atan2 b b) (* 1/2 (- b a)))))))

series431.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(sin (pow (atan2 b b) (* 1/2 (- b a))))
136.0ms	(log1p (expm1 (expm1 (log1p (sin (pow (atan2 b b) (* 1/2 (- b a))))))))
98.0ms	(expm1 (log1p (sin (pow (atan2 b b) (* 1/2 (- b a))))))
135.0ms	(expm1 (expm1 (log1p (sin (pow (atan2 b b) (* 1/2 (- b a)))))))

simplify81.0ms

Counts

54 → 54

Iterations

Useful iterations: 4 (74.0ms)

Iter	Nodes	Cost
0	143	467
1	339	409
2	946	383
3	2556	373
4	5001	363
done	5001	363

prune167.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes30.0ms

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	11	7
1	11	7
done	11	7

end0.0ms

sample2.2s

Algorithm

intervals

Results

765.0ms	1848×	body	10240	exit
457.0ms	9800×	body	80	nan
440.0ms	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