Details

sample107.0ms

Algorithm

intervals

Results

40.0ms	61×	body	10240	exit
21.0ms	285×	body	80	nan
21.0ms	255×	body	80	valid
1.0ms	1×	body	640	valid

simplify9.3s

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	117	9
5	438	9
6	4540	9
done	5001	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

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))

rewrite23.0ms

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)))
4.0ms	(sqrt (atan2 b b))

series179.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(pow (sqrt (atan2 b b)) (- b a))
111.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
32.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

57 → 57

Iterations

Useful iterations: 3 (893.0ms)

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

prune235.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

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))

rewrite87.0ms

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:

49.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
25.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
9.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series143.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
24.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
29.0ms	(pow (sqrt (atan2 b b)) (- b a))
13.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

87 → 87

Iterations

Useful iterations: 3 (1.0s)

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

prune292.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
0.0b	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
38×	`pow-unpow`
30×	`times-frac`
28×	`add-cube-cbrt`
12×	`unpow-prod-down` `sqrt-prod`
10×	`pow1`
6×	`add-exp-log` `pow-pow` `distribute-lft-out--` `difference-of-squares`
4×	`sqrt-pow1` `pow1/2` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `div-sub` `pow-exp` `sqrt-pow2` `div-inv` `pow-sub` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

9.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
13.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
3.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))

series106.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
33.0ms	(pow (sqrt (atan2 b b)) (/ (- b a) 2))
20.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify3.3s

Counts

118 → 118

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	96	1420
1	255	1286
2	832	1252
3	4335	1198
done	5001	1198

prune508.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (log (exp (+ 1 (log (pow (sqrt (atan2 b b)) (- b a)))))))
1.0b	(log (exp (+ 1 (log (pow (sqrt (atan2 b b)) (- b a))))))
1.0b	(sqrt (atan2 b b))
3.8b	(log (pow (sqrt (atan2 b b)) (- b a)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

20×	`log-prod`
13×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt`
6×	`pow1` `add-exp-log` `unpow-prod-down` `sqrt-prod` `log-pow`
5×	`log-div`
4×	`exp-prod` `sin-sum` `rem-log-exp` `add-cbrt-cube` `add-log-exp`
3×	`pow-sub`
2×	`unpow-prod-up` `associate-+r-` `exp-diff` `exp-sum`
1×	`pow-to-exp` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-exp` `sin-diff` `distribute-lft-out` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

73.0ms	(sin (log (exp (+ 1 (log (pow (sqrt (atan2 b b)) (- b a)))))))
27.0ms	(log (exp (+ 1 (log (pow (sqrt (atan2 b b)) (- b a))))))
1.0ms	(sqrt (atan2 b b))
6.0ms	(log (pow (sqrt (atan2 b b)) (- b a)))

series296.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(sin (log (exp (+ 1 (log (pow (sqrt (atan2 b b)) (- b a)))))))
53.0ms	(log (exp (+ 1 (log (pow (sqrt (atan2 b b)) (- b a))))))
12.0ms	(sqrt (atan2 b b))
100.0ms	(log (pow (sqrt (atan2 b b)) (- b a)))

simplify1.2s

Counts

79 → 79

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	141	1309
1	239	1169
2	474	1022
3	1736	1009
done	5000	1007

prune360.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes69.0ms

Accuracy

0% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	24
done	12	24

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.8s	1864×	body	10240	exit
1.5s	10128×	body	80	nan
1.3s	7989×	body	80	valid
6.0ms	2×	body	5120	valid
2.0ms	2×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid