Details

sample187.0ms

Algorithm

intervals

Results

43.0ms	65×	body	1280	valid
28.0ms	58×	body	640	valid
27.0ms	254×	body	80	valid
11.0ms	33×	body	320	valid
4.0ms	18×	body	160	valid

simplify223.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	175
8	175
7	173
6	151
5	132
4	114
3	87
2	57
1	26
0	12

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.2b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
0.4b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-r` `sqrt-prod`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative` `fma-udef`

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
26.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
10.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

series462.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(fma a1 a1 (* a2 a2))
297.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2.0)))
112.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2.0))

simplify1.8s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	2126
1	276
0	131

prune751.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cos th) (hypot a1 a2))
0.3b	(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
0.4b	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
6.4b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

81×	`sqrt-prod`
72×	`times-frac`
63×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
43×	`associate-r`
20×	`add-cbrt-cube` `add-exp-log`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`*-commutative` `div-inv`
1×	`rem-sqrt-square` `sqrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `fma-udef` `hypot-def` `unswap-sqr`

Counts

4 → 161

Calls

4 calls:

9.0ms	(* (cos th) (hypot a1 a2))
64.0ms	(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
13.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
3.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series894.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(* (cos th) (hypot a1 a2))
488.0ms	(* (* (cos th) (hypot a1 a2)) (/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0)))
194.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (sqrt 2.0))
62.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify2.7s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	3565
1	486
0	194

prune912.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize40.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.3b	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))
0.3b	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
624×	`add-sqr-sqrt`
577×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
19×	`add-cbrt-cube` `add-exp-log`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

3 → 706

Calls

3 calls:

192.0ms	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
12.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))
26.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series764.0ms

Counts

3 → 9

Calls

3 calls:

338.0ms	(* (cos th) (/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
269.0ms	(/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0)))
157.0ms	(/ (/ (fma a2 a2 (* a1 a1)) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.3s

Counts

715 → 715

Iterations

Iter	Nodes
done	5000
1	1656
0	600

prune3.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize64.0ms

Local error

Found 4 expressions with local error:

1.0b	(/ 1 (sqrt (sqrt 2.0)))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
1.0b	(cbrt 2.0)
1.0b	(cbrt 2.0)

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

867×	`sqrt-prod`
750×	`times-frac`
403×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
102×	`cbrt-prod`
34×	`associate-/l*`
21×	`associate-/r*`
17×	`add-exp-log`
15×	`div-inv`
11×	`sqrt-pow1` `add-cbrt-cube`
8×	`pow1` `div-exp`
7×	`pow-flip`
4×	`expm1-log1p-u` `cbrt-undiv` `pow1/3` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2`
2×	`rec-exp` `clear-num` `frac-2neg` `1-exp` `pow-div`
1×	`inv-pow` `associate-/l/`

Counts

4 → 523

Calls

4 calls:

7.0ms	(/ 1 (sqrt (sqrt 2.0)))
51.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
1.0ms	(cbrt 2.0)
2.0ms	(cbrt 2.0)

series0.0ms

Counts

4 → 4

Calls

4 calls:

0.0ms	(/ 1 (sqrt (sqrt 2.0)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt (cbrt 2.0))))
0.0ms	(cbrt 2.0)
0.0ms	(cbrt 2.0)

simplify1.8s

Counts

527 → 527

Iterations

Iter	Nodes
done	5000
2	3982
1	1195
0	508

prune1.9s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes551.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.4s	2548×	body	1280	valid
1.6s	2177×	body	640	valid
1.1s	7942×	body	80	valid
300.0ms	997×	body	320	valid
106.0ms	534×	body	160	valid