Details

sample538.0ms

Algorithm

intervals

Results

104.0ms	255×	body	80	valid
70.0ms	285×	body	80	nan
69.0ms	61×	body	10240	exit
1.0ms	1×	body	640	valid

simplify8.6s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	7	9
1	13	9
2	22	9
3	45	9
4	117	9
5	444	9
6	4596	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))

rewrite64.0ms

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:

28.0ms	(pow (sqrt (atan2 b b)) (- b a))
24.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
7.0ms	(sqrt (atan2 b b))

series206.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(pow (sqrt (atan2 b b)) (- b a))
132.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
33.0ms	(sqrt (atan2 b b))

simplify832.0ms

Counts

72 → 72

Iterations

Useful iterations: done (828.0ms)

Iter	Nodes	Cost
0	117	962
1	315	839
2	1100	762
done	5000	737

prune222.0ms

Pruning

3 alts after pruning (3 fresh and 0 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))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`add-cube-cbrt`
22×	`unpow-prod-up` `log-pow`
21×	`exp-prod`
18×	`prod-diff`
12×	`unpow-prod-down`
9×	`sqrt-prod`
8×	`pow1`
6×	`log-prod`
5×	`add-exp-log` `pow-unpow`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 101

Calls

4 calls:

63.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
23.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
8.0ms	(pow (sqrt (atan2 b b)) (- b a))
1.0ms	(sqrt (atan2 b b))

series212.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sin (log (exp (pow (sqrt (atan2 b b)) (- b a)))))
43.0ms	(log (exp (pow (sqrt (atan2 b b)) (- b a))))
36.0ms	(pow (sqrt (atan2 b b)) (- b a))
11.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	188	1681
1	401	1405
2	1211	1263
done	5001	1209

prune416.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (exp (expm1 (log1p (pow (sqrt (atan2 b b)) (- b a))))))
0.0b	(expm1 (log1p (pow (sqrt (atan2 b b)) (- b a))))
0.0b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

6.0ms	(log (exp (expm1 (log1p (pow (sqrt (atan2 b b)) (- b a))))))
1.0ms	(expm1 (log1p (pow (sqrt (atan2 b b)) (- b a))))
17.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series202.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(log (exp (expm1 (log1p (pow (sqrt (atan2 b b)) (- b a))))))
79.0ms	(expm1 (log1p (pow (sqrt (atan2 b b)) (- b a))))
29.0ms	(pow (sqrt (atan2 b b)) (- b a))
17.0ms	(sqrt (atan2 b b))

simplify858.0ms

Counts

95 → 95

Iterations

Useful iterations: done (853.0ms)

Iter	Nodes	Cost
0	136	1311
1	334	1066
2	1122	980
done	5000	953

prune523.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
61.1b	(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt a)
1.0ms	(sqrt (atan2 b b))
7.0ms	(sqrt (atan2 b b))
0.0ms	(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

series1.1s

Counts

4 → 12

Calls

4 calls:

296.0ms	(cbrt a)
11.0ms	(sqrt (atan2 b b))
17.0ms	(sqrt (atan2 b b))
794.0ms	(fma (- (cbrt a)) (* (cbrt a) (cbrt a)) (* (cbrt a) (* (cbrt a) (cbrt a))))

simplify843.0ms

Counts

65 → 65

Iterations

Useful iterations: done (841.0ms)

Iter	Nodes	Cost
0	59	511
1	93	431
2	252	295
3	1002	285
done	5002	264

prune381.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes82.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
done	11	13

end0.0ms

sample5.7s

Algorithm

intervals

Results

2.6s	1864×	body	10240	exit
1.2s	10128×	body	80	nan
1.1s	7989×	body	80	valid
9.0ms	2×	body	5120	valid
2.0ms	2×	body	1280	valid
2.0ms	3×	body	640	valid
1.0ms	4×	body	160	valid