Details

sample228.0ms

Algorithm

intervals

Results

81.0ms	61×	body	10240	exit
21.0ms	299×	body	80	nan
20.0ms	256×	body	80	valid

simplify9.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	444	9
6	4596	9
done	5001	9

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

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` `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:

9.0ms	(pow (sqrt (atan2 b b)) (- b a))
15.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
6.0ms	(sqrt (atan2 b b))

series179.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(pow (sqrt (atan2 b b)) (- b a))
118.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
19.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts

72 → 72

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	117	962
1	315	839
2	1100	762
done	5000	737

prune360.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`sqrt-prod`
18×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log` `unswap-sqr`
12×	`swap-sqr` `sqr-pow`
10×	`associate-r` `associate-l`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `div-sub` `log1p-expm1-u` `pow-sub` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod`

Counts

4 → 114

Calls

4 calls:

59.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
37.0ms	(* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2)))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series181.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
38.0ms	(* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2)))
12.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.5s

Counts

126 → 126

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	123	2981
1	269	2133
2	1183	1983
done	5000	1939

prune551.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(* (cos 1) (log (sqrt (atan2 b b))))
2.0b	(log (sqrt (atan2 b b)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`log-prod` `prod-diff`
17×	`distribute-rgt-in` `distribute-lft-in`
16×	`pow1`
12×	`add-exp-log` `sqrt-prod`
11×	`associate-r` `add-cbrt-cube`
6×	`log-pow`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`sub-neg` `associate-r/` `-commutative`
1×	`rem-sqrt-square` `flip3--` `rem-log-exp` `flip--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

43.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
14.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
2.0ms	(log (sqrt (atan2 b b)))

series620.0ms

Counts

4 → 12

Calls

4 calls:

262.0ms	(* (* (cos 1) (log (sqrt (atan2 b b)))) (- b a))
11.0ms	(sqrt (atan2 b b))
232.0ms	(* (cos 1) (log (sqrt (atan2 b b))))
115.0ms	(log (sqrt (atan2 b b)))

simplify2.4s

Counts

127 → 127

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	175	2047
1	437	1837
2	2665	1579
done	5000	1546

prune516.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes82.0ms

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	10	22
done	10	22

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.0s	1773×	body	10240	exit
1.7s	9770×	body	80	nan
975.0ms	7996×	body	80	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid