Details

sample135.0ms

Algorithm

intervals

Results

45.0ms	299×	body	80	nan
39.0ms	61×	body	10240	exit
20.0ms	256×	body	80	valid

simplify9.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune4.0ms

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

rewrite49.0ms

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:

11.0ms	(pow (sqrt (atan2 b b)) (- b a))
34.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series172.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(pow (sqrt (atan2 b b)) (- b a))
120.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
13.0ms	(sqrt (atan2 b b))

simplify807.0ms

Counts

72 → 72

Iterations

Useful iterations: done (804.0ms)

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

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

100×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`unpow-prod-down`
48×	`unpow-prod-up`
46×	`add-cube-cbrt` `*-un-lft-identity`
36×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
16×	`add-exp-log`
14×	`sqr-pow`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `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 → 171

Calls

4 calls:

45.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
107.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series232.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
64.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
18.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify2.9s

Counts

183 → 183

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	209	4894
1	502	3395
2	2546	3082
done	5000	3036

prune733.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* a (cos 1)) (* 1/2 (log (atan2 b b))))
0.6b	(* a (cos 1))
1.6b	(log (atan2 b b))
1.6b	(log (atan2 b b))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1` `add-exp-log`
18×	`log-prod` `add-cbrt-cube`
14×	`add-sqr-sqrt`
12×	`distribute-rgt-in` `add-cube-cbrt` `*-un-lft-identity` `distribute-lft-in`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp` `log-pow` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 84

Calls

4 calls:

59.0ms	(* (* a (cos 1)) (* 1/2 (log (atan2 b b))))
18.0ms	(* a (cos 1))
3.0ms	(log (atan2 b b))
3.0ms	(log (atan2 b b))

series475.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (* a (cos 1)) (* 1/2 (log (atan2 b b))))
153.0ms	(* a (cos 1))
83.0ms	(log (atan2 b b))
84.0ms	(log (atan2 b b))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	112	1077
1	298	1034
2	1335	878
done	5001	865

prune526.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes78.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
done	9	20

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.0s	1773×	body	10240	exit
1.6s	9770×	body	80	nan
900.0ms	7996×	body	80	valid
1.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid