Details

sample121.0ms

Algorithm

intervals

Results

40.0ms	48×	body	10240	exit
34.0ms	308×	body	80	nan
30.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1114
5	256
4	110
3	45
2	22
1	13
0	7

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2`
1×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 66

Calls

3 calls:

14.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
2.0ms	(sqrt (atan2 b b))

series138.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(pow (sqrt (atan2 b b)) (- b a))
83.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
20.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

75 → 75

Iterations

Iter	Nodes
done	5005
3	1669
2	674
1	311
0	120

prune304.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

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×	`pow-unpow` `pow-pow` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `insert-posit16` `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 → 87

Calls

4 calls:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
37.0ms	(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))

series180.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
106.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
16.0ms	(sqrt (atan2 b b))
16.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5046
3	2545
2	906
1	388
0	149

prune537.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.1b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite51.0ms

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×	`pow-unpow` `pow-pow` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `pow1/2` `insert-posit16` `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 → 87

Calls

4 calls:

12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
32.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series264.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
189.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (expm1 (log1p (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
17.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify2.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5002
3	2646
2	938
1	394
0	151

prune598.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
0.3b	(log (exp (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))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log-pow` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `exp-prod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`rem-log-exp`

Counts

4 → 60

Calls

4 calls:

29.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
6.0ms	(log (exp (sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series668.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
507.0ms	(log (exp (sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))))
19.0ms	(sqrt (atan2 b b))
27.0ms	(sqrt (atan2 b b))

simplify3.1s

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
4	2920
3	719
2	290
1	138
0	80

prune483.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes104.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	12
1	12
0	11

end0.0ms

sample7.1s

Algorithm

intervals

Results

2.6s	1855×	body	10240	exit
2.2s	10067×	body	80	nan
1.8s	7989×	body	80	valid
5.0ms	1×	body	5120	valid
3.0ms	2×	body	1280	valid
2.0ms	3×	body	320	valid
2.0ms	4×	body	160	valid
1.0ms	1×	body	640	valid