Details

sample248.0ms

Algorithm

intervals

Results

67.0ms	299×	body	80	nan
59.0ms	61×	body	10240	exit
29.0ms	256×	body	80	valid

simplify9.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	438	9
6	4540	9
done	5001	9

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

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))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `add-log-exp`
2×	`unpow-prod-up` `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 → 48

Calls

3 calls:

12.0ms	(pow (sqrt (atan2 b b)) (- b a))
31.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
9.0ms	(sqrt (atan2 b b))

series150.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(pow (sqrt (atan2 b b)) (- b a))
90.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

57 → 57

Iterations

Useful iterations: 3 (900.0ms)

Iter	Nodes	Cost
0	75	614
1	188	571
2	654	536
3	4107	527
done	5002	527

prune258.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

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))

rewrite110.0ms

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×	`div-sub` `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 → 106

Calls

4 calls:

43.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
59.0ms	(* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2)))
2.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series232.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
73.0ms	(* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2)))
17.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

118 → 118

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	117	2871
1	259	2061
2	1151	1910
done	5001	1865

prune504.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (log (sqrt (atan2 b b))) (- b a))
0.6b	(* (cos 1) (* (log (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
2.0b	(log (sqrt (atan2 b b)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1`
15×	`add-sqr-sqrt`
12×	`add-exp-log` `*-un-lft-identity`
11×	`add-cbrt-cube`
10×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
9×	`associate-l`
6×	`sub-neg` `log-prod` `associate-r/` `associate-r*` `sqrt-prod` `log-pow`
4×	`pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`sqrt-pow1` `pow1/2`
2×	`flip3--` `*-commutative` `flip--`
1×	`rem-sqrt-square` `rem-log-exp` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 87

Calls

4 calls:

26.0ms	(* (log (sqrt (atan2 b b))) (- b a))
53.0ms	(* (cos 1) (* (log (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
2.0ms	(log (sqrt (atan2 b b)))

series469.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(* (log (sqrt (atan2 b b))) (- b a))
251.0ms	(* (cos 1) (* (log (sqrt (atan2 b b))) (- b a)))
13.0ms	(sqrt (atan2 b b))
108.0ms	(log (sqrt (atan2 b b)))

simplify769.0ms

Counts

99 → 99

Iterations

Useful iterations: 2 (175.0ms)

Iter	Nodes	Cost
0	111	1232
1	252	1180
2	1082	1027
done	5000	1027

prune447.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes122.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	22
done	10	22

end0.0ms

sample5.5s

Algorithm

intervals

Results

2.1s	9770×	body	80	nan
1.5s	1773×	body	10240	exit
1.1s	7996×	body	80	valid
2.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid