Details

sample111.0ms

Algorithm

intervals

Results

38.0ms	58×	body	10240	exit
23.0ms	327×	body	80	nan
21.0ms	256×	body	80	valid

simplify3.8s

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	274	9
6	837	9
7	3217	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite44.0ms

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:

30.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
9.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series136.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
26.0ms	(pow (sqrt (atan2 b b)) (- b a))
21.0ms	(sqrt (atan2 b b))

simplify4.2s

Counts

72 → 72

Iterations

Useful iterations: 4 (2.8s)

Iter	Nodes	Cost
0	117	962
1	246	836
2	485	757
3	1266	728
4	4144	699
done	5000	699

prune251.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(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))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
93×	`sqrt-prod`
87×	`unpow-prod-down`
59×	`unpow-prod-up`
58×	`*-un-lft-identity`
56×	`add-cube-cbrt`
45×	`prod-diff`
32×	`swap-sqr`
25×	`unswap-sqr`
24×	`associate-r` `associate-l`
17×	`add-exp-log`
15×	`sqr-pow`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`expm1-log1p-u` `pow1/2` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `*-commutative` `pow-prod-up` `sqrt-pow2` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 206

Calls

4 calls:

12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
95.0ms	(* (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))

series132.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
66.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
13.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify4.0s

Counts

218 → 218

Iterations

Useful iterations: 3 (2.4s)

Iter	Nodes	Cost
0	210	5420
1	443	3874
2	1288	3547
3	4645	3437
done	5000	3437

prune686.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt b)
0.8b	(pow (cbrt b) 3)
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod` `sqrt-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow1/3`
1×	`cube-mult` `pow-to-exp` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt b)
4.0ms	(pow (cbrt b) 3)
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series596.0ms

Counts

4 → 12

Calls

4 calls:

277.0ms	(cbrt b)
288.0ms	(pow (cbrt b) 3)
12.0ms	(sqrt (atan2 b b))
18.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

87 → 87

Iterations

Useful iterations: 3 (205.0ms)

Iter	Nodes	Cost
0	73	525
1	148	374
2	281	349
3	681	345
4	2469	345
done	5000	345

prune481.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series70.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
16.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

72 → 72

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	20	424
1	25	368
2	28	360
3	32	360
4	38	360
5	48	360
6	69	360
7	147	360
8	437	360
9	1815	360
done	5001	360

prune396.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes34.0ms

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	17	27
1	20	27
done	20	27

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.4s	1777×	body	10240	exit
1.3s	9788×	body	80	nan
849.0ms	7988×	body	80	valid
16.0ms	4×	body	5120	valid
1.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid