Details

sample136.0ms

Algorithm

intervals

Results

73.0ms	82×	body	1280	valid
21.0ms	66×	body	640	valid
18.0ms	245×	body	80	valid
7.0ms	28×	body	320	valid
1.0ms	8×	body	160	valid

simplify378.0ms

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

localize22.0ms

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))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
70×	`add-sqr-sqrt`
60×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 180

Calls

4 calls:

62.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
56.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
10.0ms	(/ (cos th) (sqrt 2))
14.0ms	(/ (cos th) (sqrt 2))

series433.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
141.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
69.0ms	(/ (cos th) (sqrt 2))
88.0ms	(/ (cos th) (sqrt 2))

simplify1.6s

Counts

192 → 192

Iterations

Iter	Nodes
done	5001
2	1524
1	528
0	189

prune984.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ a1 (sqrt 2)) a1)
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.4b	(/ a1 (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
74×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l` `sqrt-prod`
25×	`add-cbrt-cube` `add-exp-log`
12×	`associate-/r*`
11×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`associate-/l*` `unswap-sqr`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `associate-r` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`

Counts

4 → 177

Calls

4 calls:

28.0ms	(* (/ a1 (sqrt 2)) a1)
47.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
6.0ms	(/ a1 (sqrt 2))
10.0ms	(/ (cos th) (sqrt 2))

series414.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* (/ a1 (sqrt 2)) a1)
165.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
84.0ms	(/ a1 (sqrt 2))
72.0ms	(/ (cos th) (sqrt 2))

simplify1.8s

Counts

189 → 189

Iterations

Iter	Nodes
done	5000
2	1683
1	546
0	219

prune977.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

616×	`sqrt-prod`
614×	`times-frac`
345×	`add-sqr-sqrt`
340×	`*-un-lft-identity` `add-cube-cbrt`
37×	`associate-/l*`
25×	`add-cbrt-cube` `add-exp-log`
24×	`associate-/r*`
22×	`associate-l`
14×	`div-inv`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 481

Calls

4 calls:

7.0ms	(/ a1 (sqrt (sqrt 2)))
50.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
45.0ms	(/ (/ a1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
21.0ms	(/ (cos th) (sqrt 2))

series448.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ a1 (sqrt (sqrt 2)))
129.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
64.0ms	(/ (/ a1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
96.0ms	(/ (cos th) (sqrt 2))

simplify2.2s

Counts

493 → 493

Iterations

Iter	Nodes
done	5000
2	2733
1	1158
0	500

prune2.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize79.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ a1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(expm1 (/ (cos th) (sqrt 2)))
0.7b	(log1p (expm1 (/ (cos th) (sqrt 2))))
0.7b	(/ (cos th) (sqrt 2))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

570×	`sqrt-prod`
567×	`times-frac`
305×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
34×	`associate-/l*`
15×	`associate-/r*`
12×	`div-inv`
11×	`add-cbrt-cube` `add-exp-log`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`log1p-udef` `expm1-log1p` `log1p-expm1` `expm1-udef` `associate-/l/`

Counts

4 → 403

Calls

4 calls:

30.0ms	(/ (/ a1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.0ms	(expm1 (/ (cos th) (sqrt 2)))
0.0ms	(log1p (expm1 (/ (cos th) (sqrt 2))))
10.0ms	(/ (cos th) (sqrt 2))

series770.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (/ a1 (sqrt (sqrt 2))) (sqrt (sqrt 2)))
225.0ms	(expm1 (/ (cos th) (sqrt 2)))
359.0ms	(log1p (expm1 (/ (cos th) (sqrt 2))))
109.0ms	(/ (cos th) (sqrt 2))

simplify2.0s

Counts

415 → 415

Iterations

Iter	Nodes
done	5003
2	2278
1	1025
0	473

prune1.9s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes595.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	17

end0.0ms

sample6.6s

Algorithm

intervals

Results

2.1s	2565×	body	1280	valid
1.8s	2148×	body	640	valid
1.0s	8111×	body	80	valid
989.0ms	1069×	body	320	valid
148.0ms	530×	body	160	valid