Details

sample216.0ms

Algorithm

intervals

Results

70.0ms	89×	body	1280	valid
59.0ms	242×	body	80	valid
49.0ms	81×	body	640	valid
14.0ms	33×	body	320	valid
3.0ms	9×	body	160	valid

simplify130.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize32.0ms

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))

rewrite103.0ms

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:

47.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
33.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms	(/ (cos th) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series466.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
137.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
71.0ms	(/ (cos th) (sqrt 2))
101.0ms	(/ (cos th) (sqrt 2))

simplify1.1s

Counts

184 → 184

Iterations

Iter	Nodes
done	2000
3	2000
2	1563
1	533
0	183

prune975.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

52×	`times-frac`
51×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 147

Calls

4 calls:

17.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
37.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
11.0ms	(/ (* a1 a1) (sqrt 2))
9.0ms	(/ (cos th) (sqrt 2))

series481.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
149.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
75.0ms	(/ (* a1 a1) (sqrt 2))
75.0ms	(/ (cos th) (sqrt 2))

simplify1.3s

Counts

159 → 159

Iterations

Iter	Nodes
done	2008
3	2008
2	1970
1	564
0	205

prune783.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
24×	`add-sqr-sqrt`
20×	`times-frac`
17×	`*-un-lft-identity` `add-cube-cbrt`
16×	`sqrt-prod`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`associate-l`
4×	`pow-prod-down` `insert-posit16` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `-commutative` `associate-/l`
1×	`associate-*r/`

Counts

4 → 111

Calls

4 calls:

35.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
17.0ms	(* (cos th) (* a2 a2))
12.0ms	(/ (* a1 a1) (sqrt 2))
37.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))

series469.0ms

Counts

4 → 12

Calls

4 calls:

173.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
58.0ms	(* (cos th) (* a2 a2))
98.0ms	(/ (* a1 a1) (sqrt 2))
141.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))

simplify1.2s

Counts

123 → 123

Iterations

Iter	Nodes
done	2006
3	2006
2	1759
1	479
0	167

prune640.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

16.0ms	(* (cos th) (* a1 a1))
29.0ms	(* (cos th) (* a2 a2))
47.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
40.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))

series417.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (cos th) (* a1 a1))
55.0ms	(* (cos th) (* a2 a2))
158.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
144.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))

simplify1.6s

Counts

112 → 112

Iterations

Iter	Nodes
done	2089
3	2089
2	1469
1	435
0	156

prune550.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes531.0ms

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	17
1	17
0	13

end0.0ms

sample8.4s

Algorithm

intervals

Results

2.9s	2556×	body	1280	valid
2.8s	2152×	body	640	valid
1.5s	7805×	body	80	valid
587.0ms	1054×	body	320	valid
173.0ms	492×	body	160	valid