Details

sample139.0ms

Algorithm

intervals

Results

47.0ms	51×	body	10240	exit
34.0ms	300×	body	80	nan
33.0ms	256×	body	80	valid

simplify1.6s

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: 0.0b

localize31.0ms

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` `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:

17.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
11.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series137.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
25.0ms	(pow (sqrt (atan2 b b)) (- b a))
20.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

75 → 75

Iterations

Iter	Nodes
done	5006
3	1724
2	687
1	311
0	120

prune319.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite22.0ms

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` `insert-posit16` `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 → 122

Calls

4 calls:

11.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
6.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series105.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
43.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
3	1980
2	766
1	338
0	124

prune617.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

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))

rewrite12.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`pow-to-exp` `pow-pow` `div-sub` `pow-exp` `div-inv` `pow-sub` `sqr-pow`

Counts

2 → 47

Calls

2 calls:

7.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
5.0ms	(pow (atan2 b b) (/ (- b a) 2))

series123.0ms

Counts

2 → 6

Calls

2 calls:

91.0ms	(sin (pow (atan2 b b) (/ (- b a) 2)))
32.0ms	(pow (atan2 b b) (/ (- b a) 2))

simplify2.2s

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	2210
2	693
1	260
0	106

prune302.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (pow (atan2 b b) (/ (- b a) 2))) (cbrt (pow (atan2 b b) (/ (- b a) 2))))
0.3b	(cbrt (pow (atan2 b b) (/ (- b a) 2)))
0.3b	(cbrt (pow (atan2 b b) (/ (- b a) 2)))
0.3b	(cbrt (pow (atan2 b b) (/ (- b a) 2)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

73×	`cbrt-prod`
46×	`add-sqr-sqrt`
29×	`unpow-prod-down`
22×	`*-un-lft-identity` `add-cube-cbrt`
16×	`unswap-sqr`
15×	`sqr-pow`
11×	`pow1`
10×	`swap-sqr` `associate-r` `associate-l`
9×	`pow1/3`
7×	`cbrt-div` `div-sub` `pow-sub`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 127

Calls

4 calls:

39.0ms	(* (cbrt (pow (atan2 b b) (/ (- b a) 2))) (cbrt (pow (atan2 b b) (/ (- b a) 2))))
4.0ms	(cbrt (pow (atan2 b b) (/ (- b a) 2)))
4.0ms	(cbrt (pow (atan2 b b) (/ (- b a) 2)))
4.0ms	(cbrt (pow (atan2 b b) (/ (- b a) 2)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* (cbrt (pow (atan2 b b) (/ (- b a) 2))) (cbrt (pow (atan2 b b) (/ (- b a) 2))))
62.0ms	(cbrt (pow (atan2 b b) (/ (- b a) 2)))
51.0ms	(cbrt (pow (atan2 b b) (/ (- b a) 2)))
61.0ms	(cbrt (pow (atan2 b b) (/ (- b a) 2)))

simplify2.0s

Counts

139 → 139

Iterations

Iter	Nodes
done	5000
3	1620
2	566
1	244
0	121

prune873.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample5.4s

Algorithm

intervals

Results

2.1s	9841×	body	80	nan
1.9s	1881×	body	10240	exit
1.0s	7992×	body	80	valid
3.0ms	1×	body	5120	valid
2.0ms	2×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
1.0ms	2×	body	160	valid