Details

sample292.0ms

Algorithm

intervals

Results

93.0ms	256×	body	80	valid
71.0ms	61×	body	10240	exit
43.0ms	305×	body	80	nan

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2050
7	2050
6	1161
5	250
4	110
3	45
2	22
1	13
0	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

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))

series110.0ms

Counts

3 → 9

Calls

3 calls:

68.0ms	(sin (pow (sqrt (atan2 b b)) (- b a)))
24.0ms	(pow (sqrt (atan2 b b)) (- b a))
18.0ms	(sqrt (atan2 b b))

simplify1.0s

Counts

60 → 60

Iterations

Iter	Nodes
done	2004
4	2004
3	1051
2	391
1	184
0	78

prune697.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

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))

rewrite51.0ms

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))
33.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series132.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
50.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (pow (sqrt (sqrt (atan2 b b))) (- b a)))
20.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

178 → 178

Iterations

Iter	Nodes
done	2001
3	2001
2	1104
1	396
0	150

prune2.3s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize71.0ms

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))

rewrite7.0ms

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:

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

series56.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (atan2 b b))
16.0ms	(sqrt (atan2 b b))
15.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	2048
10	2048
9	885
8	354
7	118
6	73
5	51
4	39
3	31
2	27
1	24
0	19

prune1.2s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
57×	`prod-exp`
28×	`pow-to-exp` `pow-exp`
24×	`sqrt-prod`
21×	`add-sqr-sqrt`
15×	`unpow-prod-down` `associate-l`
12×	`pow-sub`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`frac-times` `associate-*r/` `unswap-sqr`
4×	`insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `swap-sqr` `associate-*l/` `cbrt-unprod`
2×	`unpow-prod-up` `pow-prod-down` `sqr-pow`
1×	`sub-neg` `associate-r` `*-commutative`

Counts

4 → 115

Calls

4 calls:

77.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series117.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* (pow (sqrt (sqrt (atan2 b b))) (- b a)) (* (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a)) (pow (sqrt (sqrt (sqrt (atan2 b b)))) (- b a))))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))
14.0ms	(sqrt (atan2 b b))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	2001
3	2001
2	968
1	323
0	128

prune1.8s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes60.0ms

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
done	13
1	13
0	12

end0.0ms

sample6.8s

Algorithm

intervals

Results

2.4s	1832×	body	10240	exit
2.2s	9866×	body	80	nan
1.8s	7992×	body	80	valid
6.0ms	3×	body	2560	valid
3.0ms	1×	body	5120	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid