Details

sample198.0ms

Algorithm

intervals

Results

46.0ms	46×	body	10240	exit
33.0ms	275×	body	80	nan
29.0ms	256×	body	80	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
7	2494
6	745
5	254
4	110
3	45
2	22
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

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))

rewrite20.0ms

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:

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

series166.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
31.0ms	(pow (sqrt (atan2 b b)) (- b a))
25.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

75 → 75

Iterations

Iter	Nodes
4	3500
3	1486
2	616
1	299
0	120

prune565.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

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))

rewrite31.0ms

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:

12.0ms	(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))

series125.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
46.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify2.5s

Counts

134 → 134

Iterations

Iter	Nodes
4	4382
3	1816
2	698
1	326
0	124

prune986.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `rem-sqrt-square` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 64

Calls

4 calls:

8.0ms	(sqrt (atan2 b b))
3.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series81.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify6.1s

Counts

76 → 76

Iterations

Iter	Nodes
10	6738
9	1474
8	499
7	202
6	98
5	59
4	39
3	31
2	27
1	24
0	21

prune886.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b	(sqrt (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
24×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
12×	`unpow-prod-down`
11×	`unpow-prod-up`
9×	`prod-diff`
8×	`rem-sqrt-square`
7×	`pow1`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqr-pow`
1×	`sub-neg` `sqrt-div` `pow-sub`

Counts

4 → 90

Calls

4 calls:

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

series110.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (pow (sqrt (sqrt (atan2 b b))) (- b a)))
20.0ms	(sqrt (atan2 b b))
18.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.6s

Counts

102 → 102

Iterations

Iter	Nodes
4	3340
3	1309
2	545
1	272
0	142

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	21
1	21
0	17

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.4s	1797×	body	10240	exit
2.3s	9763×	body	80	nan
1.7s	7986×	body	80	valid
8.0ms	2×	body	5120	valid
7.0ms	3×	body	2560	valid
4.0ms	3×	body	1280	valid
1.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid
0.0ms	2×	body	160	valid