Details

sample169.0ms

Algorithm

intervals

Results

58.0ms	328×	body	80	nan
55.0ms	80×	body	10240	exit
25.0ms	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(sin (pow (sqrt (atan2 b b)) (- b a)))
0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite26.0ms

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:

13.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
9.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series162.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
49.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sqrt (atan2 b b))

simplify4.2s

Counts

72 → 72

Iterations

Useful iterations: 4 (2.7s)

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

prune263.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`add-exp-log` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

27.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
19.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series134.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
48.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
20.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify5.2s

Counts

130 → 130

Iterations

Useful iterations: 4 (3.1s)

Iter	Nodes	Cost
0	120	1876
1	257	1588
2	492	1474
3	1337	1420
4	4324	1364
done	5000	1364

prune523.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
0.2b	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
36×	`prod-diff`
34×	`*-un-lft-identity`
32×	`add-cube-cbrt`
22×	`distribute-rgt-in` `distribute-lft-in` `exp-sum`
11×	`pow1`
8×	`associate-l`
6×	`add-exp-log` `sqrt-pow1` `sqrt-prod` `add-cbrt-cube`
5×	`associate-r` `log-pow` `add-log-exp`
4×	`expm1-log1p-u` `sub-neg` `pow1/2` `log1p-expm1-u`
2×	`rem-sqrt-square` `associate-*r/`
1×	`exp-prod` `flip3--` `exp-to-pow` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

23.0ms	(exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
42.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series268.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp (* (log (sqrt (sqrt (atan2 b b)))) (- b a)))
177.0ms	(* (log (sqrt (sqrt (atan2 b b)))) (- b a))
21.0ms	(sqrt (atan2 b b))
28.0ms	(sqrt (atan2 b b))

simplify3.0s

Counts

127 → 127

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	168	2344
1	338	1870
2	748	1601
3	2427	1517
done	5001	1174

prune455.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b a))
0.5b	(cbrt (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 64

Calls

4 calls:

7.0ms	(cbrt (- b a))
7.0ms	(cbrt (- b a))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series430.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(cbrt (- b a))
194.0ms	(cbrt (- b a))
12.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

76 → 76

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	89	604
1	172	564
2	332	544
3	700	518
4	1704	494
done	5001	486

prune424.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

regimes73.0ms

Accuracy

0% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 0.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	33
1	16	33
done	16	33

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.5s	1870×	body	10240	exit
1.2s	9847×	body	80	nan
1.2s	7993×	body	80	valid
5.0ms	1×	body	5120	valid
2.0ms	1×	body	2560	valid
1.0ms	2×	body	1280	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid