Details

sample177.0ms

Algorithm

intervals

Results

69.0ms	66×	body	10240	exit
44.0ms	329×	body	80	nan
30.0ms	256×	body	80	valid

simplify2.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	1122
5	256
4	110
3	45
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite55.0ms

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:

33.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
16.0ms	(pow (sqrt (atan2 b b)) (- b a))
3.0ms	(sqrt (atan2 b b))

series185.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
41.0ms	(pow (sqrt (atan2 b b)) (- b a))
22.0ms	(sqrt (atan2 b b))

simplify3.2s

Counts

72 → 72

Iterations

Iter	Nodes
done	5004
3	1713
2	682
1	308
0	117

prune522.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize47.0ms

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))

rewrite80.0ms

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

Counts

4 → 118

Calls

4 calls:

30.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
35.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series179.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
65.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
21.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify2.9s

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
3	1920
2	741
1	333
0	120

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (pow (atan2 b b) (/ (- b a) 4)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(pow (atan2 b b) (/ (- b a) 4))
1.0b	(sqrt (atan2 b b))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

68×	`add-sqr-sqrt`
45×	`*-un-lft-identity`
38×	`unpow-prod-down`
37×	`add-cube-cbrt`
30×	`sqrt-prod`
24×	`pow-unpow` `associate-r`
22×	`unpow-prod-up`
18×	`add-exp-log` `prod-diff`
15×	`times-frac` `unswap-sqr`
12×	`sqr-pow`
9×	`pow1` `prod-exp`
8×	`pow-to-exp` `pow-exp`
7×	`associate-l`
6×	`pow-pow` `add-cbrt-cube` `pow-sub`
5×	`sqrt-pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`pow1/2` `div-sub`
2×	`sub-neg`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `associate-l/` `*-commutative` `sqrt-pow2` `cbrt-unprod` `div-inv`

Counts

4 → 164

Calls

4 calls:

88.0ms	(* (pow (atan2 b b) (/ (- b a) 4)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
18.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
15.0ms	(pow (atan2 b b) (/ (- b a) 4))
3.0ms	(sqrt (atan2 b b))

series269.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (pow (atan2 b b) (/ (- b a) 4)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
74.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
41.0ms	(pow (atan2 b b) (/ (- b a) 4))
22.0ms	(sqrt (atan2 b b))

simplify3.1s

Counts

176 → 176

Iterations

Iter	Nodes
done	5001
2	1854
1	676
0	246

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b a))
0.5b	(cbrt (- b a))
0.5b	(* (cbrt (- b a)) (cbrt (- b a)))
1.0b	(sqrt (atan2 b b))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
36×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
16×	`cbrt-div`
15×	`add-cube-cbrt`
12×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 107

Calls

4 calls:

8.0ms	(cbrt (- b a))
7.0ms	(cbrt (- b a))
69.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
3.0ms	(sqrt (atan2 b b))

series822.0ms

Counts

4 → 12

Calls

4 calls:

268.0ms	(cbrt (- b a))
288.0ms	(cbrt (- b a))
245.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
21.0ms	(sqrt (atan2 b b))

simplify3.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5001
3	2056
2	731
1	312
0	152

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes181.0ms

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	16
1	16
0	15

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.0s	9825×	body	80	nan
2.1s	1825×	body	10240	exit
1.4s	7982×	body	80	valid
10.0ms	2×	body	5120	valid
4.0ms	3×	body	1280	valid
3.0ms	3×	body	640	valid
2.0ms	6×	body	160	valid
2.0ms	1×	body	2560	valid
1.0ms	3×	body	320	valid