Details

sample369.0ms

Algorithm

intervals

Results

124.0ms	61×	body	10240	exit
103.0ms	256×	body	80	valid
56.0ms	305×	body	80	nan

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
7	2433
6	740
5	248
4	110
3	45
2	22
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`pow1` `unpow-prod-down` `sqrt-prod`
5×	`pow-unpow`
4×	`add-exp-log`
3×	`pow-pow` `add-cbrt-cube` `insert-posit16` `add-log-exp`
2×	`unpow-prod-up` `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 → 51

Calls

3 calls:

13.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
5.0ms	(pow (sqrt (atan2 b b)) (- b a))
2.0ms	(sqrt (atan2 b b))

series135.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
30.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify922.0ms

Counts

60 → 60

Iterations

Iter	Nodes
4	2133
3	900
2	409
1	182
0	78

prune382.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

93×	`sqrt-prod`
87×	`unpow-prod-down`
82×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`add-cube-cbrt`
25×	`unswap-sqr`
23×	`swap-sqr`
17×	`add-exp-log`
15×	`associate-r` `associate-l` `sqr-pow`
14×	`unpow-prod-up`
9×	`pow1` `prod-exp`
7×	`pow-to-exp` `sub-neg` `pow-exp`
6×	`sqrt-pow1` `add-cbrt-cube`
5×	`pow-unpow` `pow-pow` `pow-sub`
4×	`pow1/2` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square`
1×	`pow2` `frac-times` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 166

Calls

4 calls:

11.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
47.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series139.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
54.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
19.0ms	(sqrt (atan2 b b))
19.0ms	(sqrt (atan2 b b))

simplify3.3s

Counts

178 → 178

Iterations

Iter	Nodes
3	3182
2	1075
1	392
0	150

prune560.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

2.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series92.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (atan2 b b))
27.0ms	(sqrt (atan2 b b))
21.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify6.3s

Counts

68 → 68

Iterations

Iter	Nodes
10	6978
9	1473
8	463
7	195
6	96
5	57
4	37
3	29
2	25
1	22
0	19

prune490.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (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

27×	`sqrt-prod`
17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`unpow-prod-down` `sqrt-pow1` `add-cube-cbrt`
11×	`pow1`
7×	`pow-pow`
6×	`pow1/2`
5×	`pow-unpow` `add-exp-log`
4×	`add-cbrt-cube` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square`
2×	`unpow-prod-up`
1×	`pow-to-exp` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 81

Calls

4 calls:

6.0ms	(pow (sqrt (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))

series87.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
13.0ms	(sqrt (atan2 b b))

simplify2.3s

Counts

93 → 93

Iterations

Iter	Nodes
4	3348
3	1368
2	589
1	249
0	99

prune485.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes83.0ms

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
2	13
1	13
0	12

end0.0ms

sample7.0s

Algorithm

intervals

Results

3.0s	1832×	body	10240	exit
1.8s	9866×	body	80	nan
1.8s	7992×	body	80	valid
8.0ms	3×	body	2560	valid
6.0ms	1×	body	5120	valid
3.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid