Details

sample136.0ms

Algorithm

intervals

Results

51.0ms	326×	body	80	nan
41.0ms	56×	body	10240	exit
21.0ms	256×	body	80	valid

simplify3.6s

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	115	9
5	268	9
6	834	9
7	3197	9
done	5001	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite41.0ms

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:

15.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series135.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(pow (sqrt (atan2 b b)) (- b a))
83.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
17.0ms	(sqrt (atan2 b b))

simplify2.2s

Counts

57 → 57

Iterations

Useful iterations: 3 (309.0ms)

Iter	Nodes	Cost
0	75	614
1	147	571
2	337	536
3	843	527
4	2738	527
done	5000	527

prune162.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

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))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-prod`
78×	`unpow-prod-down`
76×	`add-sqr-sqrt`
25×	`unswap-sqr`
23×	`swap-sqr`
22×	`add-cube-cbrt` `*-un-lft-identity`
16×	`add-exp-log`
15×	`associate-r` `associate-l`
14×	`sqr-pow`
12×	`unpow-prod-up`
9×	`prod-exp`
6×	`pow1` `pow-to-exp` `sub-neg` `pow-exp` `add-cbrt-cube`
4×	`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 → 136

Calls

4 calls:

34.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
53.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series199.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
60.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify2.9s

Counts

148 → 148

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	141	3640
1	281	2623
2	957	2461
3	3812	2409
done	5001	2400

prune297.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin (cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3)))
0.0b	(cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3))
0.0b	(pow (pow (sqrt (atan2 b b)) (- b a)) 3)
1.0b	(sqrt (atan2 b b))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

48×	`unpow-prod-down`
30×	`cbrt-prod`
24×	`cube-prod`
20×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
15×	`sqrt-prod`
8×	`unpow-prod-up`
6×	`add-exp-log` `sqr-pow`
5×	`pow1` `add-cbrt-cube`
4×	`sub-neg` `pow-exp` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `pow-to-exp` `unpow3` `pow-sub`
1×	`rem-sqrt-square` `cbrt-div` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 104

Calls

4 calls:

29.0ms	(sin (cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3)))
9.0ms	(cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3))
9.0ms	(pow (pow (sqrt (atan2 b b)) (- b a)) 3)
1.0ms	(sqrt (atan2 b b))

series143.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(sin (cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3)))
26.0ms	(cbrt (pow (pow (sqrt (atan2 b b)) (- b a)) 3))
42.0ms	(pow (pow (sqrt (atan2 b b)) (- b a)) 3)
12.0ms	(sqrt (atan2 b b))

simplify3.2s

Counts

116 → 116

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	125	1985
1	287	1540
2	774	1505
3	4520	1480
done	5001	1480

prune206.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes25.0ms

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	9	20
done	9	20

end0.0ms

sample3.6s

Algorithm

intervals

Results

1.4s	9743×	body	80	nan
1.0s	1782×	body	10240	exit
705.0ms	7992×	body	80	valid
1.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	320	valid