Details

sample223.0ms

Algorithm

intervals

Results

78.0ms	76×	body	1280	valid
56.0ms	257×	body	80	valid
47.0ms	61×	body	640	valid
15.0ms	30×	body	320	valid
5.0ms	12×	body	160	valid

simplify186.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite179.0ms

Algorithm

rewrite-expression-head

Rules

160×	`add-sqr-sqrt`
92×	`times-frac`
76×	`*-un-lft-identity` `add-cube-cbrt`
58×	`sqrt-prod`
50×	`associate-l`
38×	`unswap-sqr`
36×	`associate-r`
32×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r` `associate-l/`
14×	`pow1`
12×	`swap-sqr` `prod-exp` `cbrt-unprod` `associate-/l*`
10×	`*-commutative`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

4 → 254

Calls

4 calls:

84.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
62.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
15.0ms	(/ (cos th) (sqrt 2))
11.0ms	(/ (cos th) (sqrt 2))

series490.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
169.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
96.0ms	(/ (cos th) (sqrt 2))
86.0ms	(/ (cos th) (sqrt 2))

simplify2.0s

Counts

266 → 266

Iterations

Iter	Nodes
done	5000
2	2576
1	863
0	256

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 2) (cos th))
0.3b	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

682×	`times-frac`
469×	`add-sqr-sqrt`
381×	`*-un-lft-identity` `add-cube-cbrt`
188×	`sqrt-prod`
94×	`associate-l`
87×	`associate-r`
75×	`swap-sqr`
42×	`unswap-sqr`
40×	`associate-/r*`
33×	`associate-/l*`
32×	`add-cbrt-cube` `add-exp-log`
28×	`*-commutative`
20×	`div-inv`
12×	`associate-*l/` `associate-/r/`
10×	`cbrt-undiv` `div-exp`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod`
5×	`clear-num` `frac-2neg`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`

Counts

4 → 569

Calls

4 calls:

14.0ms	(/ (sqrt 2) (cos th))
35.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
59.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
11.0ms	(/ (cos th) (sqrt 2))

series456.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (sqrt 2) (cos th))
149.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
154.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
85.0ms	(/ (cos th) (sqrt 2))

simplify1.8s

Counts

581 → 581

Iterations

Iter	Nodes
done	5001
1	2118
0	665

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
0.7b	(/ (cos th) (sqrt (sqrt 2)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

rewrite525.0ms

Algorithm

rewrite-expression-head

Rules

1848×	`times-frac`
1422×	`sqrt-prod`
1221×	`add-sqr-sqrt`
938×	`*-un-lft-identity` `add-cube-cbrt`
355×	`associate-l`
102×	`unswap-sqr`
92×	`associate-/l*`
87×	`associate-r`
85×	`swap-sqr`
70×	`associate-/r*`
58×	`associate-*l/`
44×	`add-cbrt-cube` `add-exp-log`
40×	`div-inv`
38×	`*-commutative`
30×	`associate-/l/`
16×	`cbrt-undiv` `div-exp`
12×	`associate-/r/`
11×	`prod-exp` `cbrt-unprod`
9×	`pow1`
7×	`clear-num` `frac-2neg`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`

Counts

4 → 1251

Calls

4 calls:

51.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
296.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
22.0ms	(/ (cos th) (sqrt (sqrt 2)))
42.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
157.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a2 a2))
136.0ms	(/ (cos th) (sqrt (sqrt 2)))
82.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))

simplify3.2s

Counts

1263 → 1263

Iterations

Iter	Nodes
done	5000
1	3616
0	1102

prune5.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
0.3b	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a2 a2))
1.0b	(/ 1 (sqrt (sqrt 2)))
1.0b	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

rewrite879.0ms

Algorithm

rewrite-expression-head

Rules

2351×	`times-frac`
1931×	`sqrt-prod`
1654×	`add-sqr-sqrt`
1176×	`*-un-lft-identity`
1116×	`add-cube-cbrt`
454×	`cbrt-prod`
448×	`associate-l`
198×	`unswap-sqr`
101×	`swap-sqr`
92×	`associate-/l*`
87×	`associate-r`
76×	`associate-/r*`
64×	`add-exp-log`
61×	`associate-*l/`
54×	`*-commutative`
46×	`div-inv`
44×	`add-cbrt-cube`
30×	`associate-/l/`
26×	`div-exp`
17×	`prod-exp`
16×	`cbrt-undiv`
13×	`pow1`
12×	`associate-/r/`
11×	`cbrt-unprod`
7×	`clear-num` `frac-2neg` `sqrt-pow1` `pow-flip`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/2` `pow-prod-down`
2×	`pow1/3` `pow-div`
1×	`inv-pow`

Counts

4 → 1539

Calls

4 calls:

62.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
279.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a2 a2))
9.0ms	(/ 1 (sqrt (sqrt 2)))
36.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

series731.0ms

Counts

4 → 8

Calls

4 calls:

154.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
577.0ms	(* (/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2)))) (* a2 a2))
0.0ms	(/ 1 (sqrt (sqrt 2)))
0.0ms	(/ (/ 1 (sqrt (sqrt 2))) (sqrt (cbrt (sqrt 2))))

simplify3.9s

Counts

1547 → 1547

Iterations

Iter	Nodes
done	5002
1	3861
0	1223

prune7.6s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes499.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample8.1s

Algorithm

intervals

Results

3.4s	2449×	body	1280	valid
1.8s	2010×	body	640	valid
1.6s	7946×	body	80	valid
592.0ms	980×	body	320	valid
228.0ms	521×	body	160	valid