Details

sample188.0ms

Algorithm

intervals

Results

62.0ms	64×	body	1280	valid
52.0ms	54×	body	640	valid
39.0ms	249×	body	80	valid
13.0ms	27×	body	320	valid
5.0ms	13×	body	160	valid

simplify141.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
0.4b	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
92×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
48×	`sqrt-prod`
25×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
2×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/`

Counts

2 → 151

Calls

2 calls:

10.0ms	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
7.0ms	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))

series694.0ms

Counts

2 → 6

Calls

2 calls:

582.0ms	(/ (cos th) (/ (sqrt 2) (fma a1 a1 (* a2 a2))))
112.0ms	(/ (sqrt 2) (fma a1 a1 (* a2 a2)))

simplify1.5s

Counts

157 → 157

Iterations

Iter	Nodes
done	5004
2	1635
1	553
0	226

prune838.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2)))
0.4b	(/ (fma a1 a1 (* a2 a2)) (sqrt 2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
38×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
22×	`associate-r` `sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`pow1`
3×	`associate-l` `associate-/l*` `unswap-sqr`
2×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`clear-num` `frac-2neg` `pow-prod-down` `associate-r/` `-commutative`

Counts

2 → 87

Calls

2 calls:

20.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2)))
5.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2))

series433.0ms

Counts

2 → 6

Calls

2 calls:

298.0ms	(* (cos th) (/ (fma a1 a1 (* a2 a2)) (sqrt 2)))
135.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt 2))

simplify2.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5003
3	2298
2	791
1	277
0	127

prune585.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2)))))
0.5b	(/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2))))
7.8b	(sqrt (fma a1 a1 (* a2 a2)))
7.8b	(sqrt (fma a1 a1 (* a2 a2)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

528×	`times-frac`
423×	`sqrt-prod`
293×	`add-sqr-sqrt`
291×	`*-un-lft-identity` `add-cube-cbrt`
46×	`associate-/r*`
12×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`div-inv`
6×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-undiv`
2×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-udef` `hypot-def`
1×	`associate-/r/`

Counts

4 → 403

Calls

4 calls:

8.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2)))))
9.0ms	(/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2))))
1.0ms	(sqrt (fma a1 a1 (* a2 a2)))
1.0ms	(sqrt (fma a1 a1 (* a2 a2)))

series392.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sqrt (fma a1 a1 (* a2 a2))) (/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2)))))
124.0ms	(/ (sqrt 2) (sqrt (fma a1 a1 (* a2 a2))))
58.0ms	(sqrt (fma a1 a1 (* a2 a2)))
77.0ms	(sqrt (fma a1 a1 (* a2 a2)))

simplify2.0s

Counts

415 → 415

Iterations

Iter	Nodes
done	5001
2	1993
1	921
0	370

prune2.0s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 3 expressions with local error:

0.1b	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
0.3b	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2)))
0.3b	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite92.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `associate-r/` `-commutative` `associate-/l/`

Counts

3 → 709

Calls

3 calls:

30.0ms	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
5.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2)))
15.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series650.0ms

Counts

3 → 9

Calls

3 calls:

284.0ms	(* (cos th) (/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))))
212.0ms	(/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2)))
154.0ms	(/ (/ (fma a1 a1 (* a2 a2)) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify2.9s

Counts

718 → 718

Iterations

Iter	Nodes
done	5028
2	3993
1	1624
0	602

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes335.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample8.3s

Algorithm

intervals

Results

3.3s	2488×	body	1280	valid
2.4s	2069×	body	640	valid
1.5s	7948×	body	80	valid
537.0ms	1037×	body	320	valid
198.0ms	511×	body	160	valid