Details

sample139.0ms

Algorithm

intervals

Results

47.0ms	45×	body	10240	exit
33.0ms	331×	body	80	nan
31.0ms	256×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

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:

12.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
16.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series146.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
38.0ms	(pow (sqrt (atan2 b b)) (- b a))
13.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
2	1098
1	315
0	117

prune323.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 118

Calls

4 calls:

9.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
12.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series129.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
52.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
2	1255
1	345
0	122

prune737.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 2 expressions with local error:

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

rewrite21.0ms

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	(sin (pow (atan2 b b) (/ (- b a) 2)))
12.0ms	(pow (atan2 b b) (/ (- b a) 2))

series111.0ms

Counts

2 → 6

Calls

2 calls:

88.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
23.0ms	(pow (atan2 b b) (/ (- b a) 2))

simplify2.3s

Counts

51 → 51

Iterations

Iter	Nodes
done	5001
3	3330
2	767
1	262
0	104

prune316.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (* (cbrt 2) (cbrt 2)))
1.0b	(cbrt 2)
1.0b	(cbrt 2)
1.0b	(cbrt 2)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log`
12×	`pow1`
9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `pow1/3` `add-cube-cbrt` `pow-flip`
7×	`add-cbrt-cube`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/l*`
2×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `cbrt-unprod` `div-inv` `inv-pow`

Counts

4 → 76

Calls

4 calls:

18.0ms	(/ 1 (* (cbrt 2) (cbrt 2)))
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)
1.0ms	(cbrt 2)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ 1 (* (cbrt 2) (cbrt 2)))
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)
0.0ms	(cbrt 2)

simplify3.2s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
3	4373
2	478
1	147
0	68

prune496.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes126.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample4.7s

Algorithm

intervals

Results

2.1s	1746×	body	10240	exit
1.1s	9649×	body	80	nan
882.0ms	7986×	body	80	valid
5.0ms	1×	body	5120	valid
2.0ms	4×	body	640	valid
1.0ms	1×	body	1280	valid
1.0ms	4×	body	320	valid
1.0ms	4×	body	160	valid