Details

sample265.0ms

Algorithm

intervals

Results

44.0ms	61×	body	10240	exit
25.0ms	285×	body	80	nan
23.0ms	255×	body	80	valid
1.0ms	1×	body	640	valid

simplify10.1s

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite32.0ms

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:

7.0ms	(pow (sqrt (atan2 b b)) (- b a))
10.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(sqrt (atan2 b b))

series167.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(pow (sqrt (atan2 b b)) (- b a))
96.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
22.0ms	(sqrt (atan2 b b))

simplify2.7s

Counts

57 → 57

Iterations

Useful iterations: 3 (961.0ms)

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

prune249.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
0.2b	(sin (* (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))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
19×	`pow-unpow`
17×	`add-cube-cbrt`
15×	`times-frac`
9×	`sqrt-prod`
8×	`pow1`
6×	`unpow-prod-down`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`pow-pow` `sqrt-pow1` `pow1/2` `distribute-lft-out--` `difference-of-squares`
2×	`rem-sqrt-square`
1×	`pow-to-exp` `div-sub` `pow-exp` `sqrt-pow2` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

9.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
52.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series201.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
125.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (pow (sqrt (atan2 b b)) (/ (- b a) 2))))
15.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify3.5s

Counts

85 → 85

Iterations

Useful iterations: 3 (1.7s)

Iter	Nodes	Cost
0	113	1090
1	289	919
2	896	842
3	4531	794
done	5001	794

prune400.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt` `log-pow`
12×	`unpow-prod-down` `exp-prod`
9×	`sqrt-prod`
8×	`pow1`
6×	`log-prod`
5×	`add-exp-log` `pow-unpow`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
3×	`pow-pow` `sin-sum`
2×	`sub-neg` `sqrt-pow1` `pow1/2` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `rem-log-exp` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

34.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
12.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
7.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series192.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
34.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
24.0ms	(pow (sqrt (atan2 b b)) (- b a))
12.0ms	(sqrt (atan2 b b))

simplify2.8s

Counts

87 → 87

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	126	1139
1	252	998
2	762	909
3	4634	900
done	5001	900

prune303.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (+ 1 (log (sqrt (pow (sqrt (atan2 b b)) (- b a)))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
3.8b	(log (sqrt (pow (sqrt (atan2 b b)) (- b a))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

21×	`sqrt-prod`
15×	`log-prod`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`unpow-prod-down`
5×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
3×	`sqrt-pow1` `pow1/2` `log-pow`
2×	`unpow-prod-up` `rem-sqrt-square` `sin-sum`
1×	`distribute-rgt-in` `sub-neg` `log-div` `distribute-lft-in` `sqrt-div` `rem-log-exp` `pow-sub` `sqr-pow`

Counts

4 → 62

Calls

4 calls:

25.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (+ 1 (log (sqrt (pow (sqrt (atan2 b b)) (- b a)))))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
12.0ms	(log (sqrt (pow (sqrt (atan2 b b)) (- b a))))

series377.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(sin (* (pow (sqrt (atan2 b b)) (/ (- b a) 2)) (+ 1 (log (sqrt (pow (sqrt (atan2 b b)) (- b a)))))))
17.0ms	(sqrt (atan2 b b))
18.0ms	(sqrt (atan2 b b))
98.0ms	(log (sqrt (pow (sqrt (atan2 b b)) (- b a))))

simplify1.2m

Counts

74 → 74

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	125	1177
1	212	1106
2	557	1015
3	4849	1004
done	5002	1004

prune218.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes63.0ms

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	10	22
done	10	22

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.0s	1864×	body	10240	exit
798.0ms	10128×	body	80	nan
653.0ms	7989×	body	80	valid
6.0ms	2×	body	5120	valid
1.0ms	2×	body	1280	valid
1.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid

Details

sample265.0ms

simplify10.1s

prune7.0ms

localize25.0ms

rewrite32.0ms

series167.0ms

simplify2.7s

prune249.0ms

localize31.0ms

rewrite67.0ms

series201.0ms

simplify3.5s

prune400.0ms

localize26.0ms

rewrite56.0ms

series192.0ms

simplify2.8s

prune303.0ms

localize43.0ms

rewrite43.0ms

series377.0ms

simplify1.2m

prune218.0ms

regimes63.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.0s

end8.4m