Details

sample232.0ms

Algorithm

intervals

Results

83.0ms	76×	body	640	valid
66.0ms	69×	body	1280	valid
40.0ms	269×	body	80	valid
20.0ms	38×	body	320	valid
3.0ms	10×	body	160	valid

simplify135.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	113
7	113
6	101
5	91
4	79
3	70
2	48
1	25
0	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 4 expressions with local error:

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

rewrite422.0ms

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×	`insert-posit16` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 172

Calls

4 calls:

23.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
40.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
16.0ms	(/ (cos th) (sqrt 2))
21.0ms	(/ (cos th) (sqrt 2))

series500.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
178.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
80.0ms	(/ (cos th) (sqrt 2))
87.0ms	(/ (cos th) (sqrt 2))

simplify3.0s

Counts

184 → 184

Iterations

Iter	Nodes
3	7244
2	1771
1	523
0	183

prune2.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a2 (cos th))
0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.3b	(/ (* a2 (* a2 (cos th))) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
44×	`times-frac`
38×	`*-un-lft-identity` `add-cube-cbrt`
29×	`add-cbrt-cube` `add-exp-log`
28×	`sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1`
10×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp`
4×	`associate-r` `pow-prod-down` `insert-posit16` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*l/`

Counts

4 → 135

Calls

4 calls:

17.0ms	(* a2 (cos th))
42.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
40.0ms	(/ (* a2 (* a2 (cos th))) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* a2 (cos th))
166.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
123.0ms	(/ (* a2 (* a2 (cos th))) (sqrt 2))
61.0ms	(/ (cos th) (sqrt 2))

simplify3.7s

Counts

147 → 147

Iterations

Iter	Nodes
3	7596
2	1758
1	527
0	203

prune1.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize30.0ms

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))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
78×	`add-sqr-sqrt`
73×	`*-un-lft-identity` `add-cube-cbrt`
52×	`sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
31×	`associate-/r*`
22×	`associate-l`
10×	`cbrt-undiv` `div-exp` `associate-/l*`
9×	`pow1`
8×	`prod-exp` `cbrt-unprod`
6×	`div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `unswap-sqr`
1×	`associate-r` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 191

Calls

4 calls:

10.0ms	(/ (sqrt 2) (cos th))
23.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
44.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
8.0ms	(/ (cos th) (sqrt 2))

series423.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (sqrt 2) (cos th))
125.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
150.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
69.0ms	(/ (cos th) (sqrt 2))

simplify707.0ms

Counts

203 → 203

Iterations

Iter	Nodes
2	2368
1	695
0	263

prune2.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
82×	`add-sqr-sqrt`
74×	`*-un-lft-identity` `add-cube-cbrt`
52×	`sqrt-prod`
31×	`associate-/r*`
25×	`add-cbrt-cube` `add-exp-log`
22×	`associate-l`
10×	`associate-/l*`
9×	`cbrt-undiv` `div-exp`
6×	`pow1` `div-inv`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `unswap-sqr`
1×	`pow-prod-down` `associate-l/` `associate-/r/` `-commutative`

Counts

4 → 188

Calls

4 calls:

5.0ms	(/ (sqrt 2) (cos th))
11.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
21.0ms	(* (/ (cos th) (sqrt 2)) a2)
24.0ms	(/ (cos th) (sqrt 2))

series419.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (sqrt 2) (cos th))
133.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
151.0ms	(* (/ (cos th) (sqrt 2)) a2)
74.0ms	(/ (cos th) (sqrt 2))

simplify732.0ms

Counts

200 → 200

Iterations

Iter	Nodes
2	2040
1	645
0	257

prune2.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes307.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
2	19
1	19
0	16

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.7s	2546×	body	1280	valid
1.7s	2111×	body	640	valid
1.6s	7993×	body	80	valid
632.0ms	1030×	body	320	valid
601.0ms	523×	body	160	valid