Details

sample65.0ms

Algorithm

intervals

Results

18.0ms	42×	body	10240	exit
14.0ms	318×	body	80	nan
13.0ms	253×	body	80	valid
0.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid
0.0ms	1×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	5
1	22	5
2	44	5
3	114	5
4	321	5
5	1627	5
6	5001	5
done	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.5b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite23.0ms

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:

8.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0ms	(sqrt (atan2 b b))

series100.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(pow (sqrt (atan2 b b)) (- b a))
66.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(sqrt (atan2 b b))

simplify73.0ms

Counts

72 → 72

Iterations

Useful iterations: 3 (67.0ms)

Iter	Nodes	Cost
0	255	514
1	714	433
2	2703	425
3	5001	408
done	5001	408

prune154.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.6b	(sin (* (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))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`pow1` `unpow-prod-down` `prod-diff`
6×	`sqrt-pow1`
5×	`add-exp-log` `pow-unpow` `pow-pow`
4×	`expm1-log1p-u` `pow1/2` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 83

Calls

4 calls:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
30.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
1.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series149.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
95.0ms	(sin (* (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))

simplify115.0ms

Counts

95 → 95

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	308	751
1	889	651
2	4114	639
3	5002	636
done	5002	636

prune270.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod` `add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

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

series337.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(cbrt (atan2 b b))
109.0ms	(cbrt (atan2 b b))
107.0ms	(cbrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify103.0ms

Counts

66 → 66

Iterations

Useful iterations: 5 (100.0ms)

Iter	Nodes	Cost
0	39	233
1	74	217
2	154	211
3	521	211
4	2941	211
5	5002	210
done	5002	210

prune310.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.5b	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`sqrt-prod`
11×	`unpow-prod-up`
9×	`unpow-prod-down` `prod-diff`
6×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `sub-neg` `log-div` `pow-exp` `log-pow` `pow-sub` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

50.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
8.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

series210.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (exp (log (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
89.0ms	(log (pow (sqrt (sqrt (atan2 b b))) (- b a)))

simplify102.0ms

Counts

89 → 89

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	337	829
1	838	695
2	3652	687
3	5002	661
done	5002	661

prune267.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

regimes57.0ms

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	20	23
1	20	23
done	20	23

end0.0ms

sample2.3s

Algorithm

intervals

Results

726.0ms	1736×	body	10240	exit
599.0ms	9724×	body	80	nan
437.0ms	7993×	body	80	valid
1.0ms	2×	body	640	valid
0.0ms	3×	body	160	valid
0.0ms	2×	body	320	valid