Details

sample292.0ms

Algorithm

intervals

Results

98.0ms	360×	body	80	nan
59.0ms	58×	body	10240	exit
32.0ms	255×	body	80	valid
0.0ms	1×	body	320	valid

simplify638.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	444
4	117
3	45
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
0.2b	(sin (pow (sqrt (atan2 b b)) (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite22.0ms

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` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

3 → 63

Calls

3 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
9.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
3.0ms	(sqrt (atan2 b b))

series149.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(pow (sqrt (atan2 b b)) (- b a))
105.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
18.0ms	(sqrt (atan2 b b))

simplify797.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1102
1	315
0	117

prune382.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.2b	(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` `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:

14.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
29.0ms	(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))

series242.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
148.0ms	(sin (* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a))))
19.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify891.0ms

Counts

95 → 95

Iterations

Iter	Nodes
done	5001
2	1427
1	391
0	146

prune520.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(pow (atan2 b b) (/ (- b a) 2))
0.3b	(sin (pow (atan2 b b) (/ (- b a) 2)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`pow-unpow`
18×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
3×	`pow1` `unpow-prod-down` `add-exp-log` `distribute-lft-out--` `difference-of-squares`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 45

Calls

2 calls:

7.0ms	(pow (atan2 b b) (/ (- b a) 2))
6.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

series134.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(pow (atan2 b b) (/ (- b a) 2))
109.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))

simplify2.1s

Counts

51 → 51

Iterations

Iter	Nodes
done	5000
3	3274
2	765
1	262
0	104

prune284.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(sin (* (pow (* (cbrt (atan2 b b)) (cbrt (atan2 b b))) (* (- b a) 1/2)) (pow (cbrt (atan2 b b)) (* (- b a) 1/2))))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))
1.0b	(cbrt (atan2 b b))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 48

Calls

4 calls:

40.0ms	(sin (* (pow (* (cbrt (atan2 b b)) (cbrt (atan2 b b))) (* (- b a) 1/2)) (pow (cbrt (atan2 b b)) (* (- b a) 1/2))))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))
1.0ms	(cbrt (atan2 b b))

series717.0ms

Counts

4 → 12

Calls

4 calls:

248.0ms	(sin (* (pow (* (cbrt (atan2 b b)) (cbrt (atan2 b b))) (* (- b a) 1/2)) (pow (cbrt (atan2 b b)) (* (- b a) 1/2))))
162.0ms	(cbrt (atan2 b b))
155.0ms	(cbrt (atan2 b b))
152.0ms	(cbrt (atan2 b b))

simplify1.5s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
3	2055
2	477
1	151
0	67

prune337.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes139.0ms

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	14
1	14
0	12

end0.0ms

sample5.3s

Algorithm

intervals

Results

1.6s	1790×	body	10240	exit
1.6s	9657×	body	80	nan
1.4s	7991×	body	80	valid
2.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	1280	valid
1.0ms	1×	body	640	valid