Details

sample229.0ms

Algorithm

intervals

Results

76.0ms	82×	body	1280	valid
72.0ms	63×	body	640	valid
37.0ms	247×	body	80	valid
18.0ms	36×	body	320	valid
5.0ms	14×	body	160	valid

simplify124.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (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))

rewrite75.0ms

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))
22.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms	(/ (cos th) (sqrt 2))
16.0ms	(/ (cos th) (sqrt 2))

series463.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
141.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
89.0ms	(/ (cos th) (sqrt 2))
69.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

184 → 184

Iterations

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

prune1.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (/ (* a1 a1) (sqrt 2)))
0.2b	(/ (* a1 a1) (sqrt 2))
0.3b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))

rewrite85.0ms

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:

35.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
12.0ms	(/ (* a1 a1) (sqrt 2))
21.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
13.0ms	(/ (cos th) (sqrt 2))

series562.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(* (cos th) (/ (* a1 a1) (sqrt 2)))
106.0ms	(/ (* a1 a1) (sqrt 2))
176.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
102.0ms	(/ (cos th) (sqrt 2))

simplify1.5s

Counts

159 → 159

Iterations

Iter	Nodes
done	2012
3	2012
2	1963
1	570
0	205

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
78×	`add-sqr-sqrt`
73×	`*-un-lft-identity` `add-cube-cbrt`
52×	`add-exp-log`
43×	`add-cbrt-cube` `sqrt-prod`
42×	`cbrt-prod`
32×	`associate-r`
23×	`associate-l`
22×	`prod-exp` `cbrt-unprod`
15×	`associate-/r*`
14×	`pow1`
12×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/l*`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`associate-*r/` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-l/` `-commutative`
1×	`frac-times`

Counts

4 → 200

Calls

4 calls:

116.0ms	(* (* (cos th) (/ a1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ a1 (cbrt (sqrt 2))))
5.0ms	(/ a1 (cbrt (sqrt 2)))
39.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
17.0ms	(/ (cos th) (sqrt 2))

series954.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (* (cos th) (/ a1 (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))) (/ a1 (cbrt (sqrt 2))))
524.0ms	(/ a1 (cbrt (sqrt 2)))
162.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
82.0ms	(/ (cos th) (sqrt 2))

simplify1.4s

Counts

212 → 212

Iterations

Iter	Nodes
done	2001
2	2001
1	839
0	297

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize52.0ms

Local error

Found 4 expressions with local error:

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

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

185×	`times-frac`
101×	`add-sqr-sqrt`
95×	`cbrt-prod`
93×	`*-un-lft-identity` `add-cube-cbrt`
67×	`sqrt-prod`
52×	`associate-l`
25×	`add-exp-log`
23×	`add-cbrt-cube`
22×	`div-inv`
16×	`pow1`
7×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `associate-/l*`
6×	`associate-/r*`
5×	`unswap-sqr`
4×	`associate-r` `pow-prod-down` `insert-posit16` `add-log-exp`
3×	`swap-sqr`
2×	`cbrt-div` `*-commutative`
1×	`pow2` `sqr-cos` `clear-num` `frac-2neg` `pow-plus` `pow1/3` `associate-*l/` `pow-sqr` `cos-mult` `pow-prod-up` `associate-/l/`

Counts

4 → 229

Calls

4 calls:

19.0ms	(* (cos th) (cos th))
42.0ms	(* (cbrt (/ (/ (* (cos th) (* (cos th) (cos th))) 2) (sqrt 2))) (* a2 a2))
16.0ms	(cbrt (/ (/ (* (cos th) (* (cos th) (cos th))) 2) (sqrt 2)))
45.0ms	(/ (/ (* (cos th) (* (cos th) (cos th))) 2) (sqrt 2))

series1.2s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (cos th) (cos th))
567.0ms	(* (cbrt (/ (/ (* (cos th) (* (cos th) (cos th))) 2) (sqrt 2))) (* a2 a2))
459.0ms	(cbrt (/ (/ (* (cos th) (* (cos th) (cos th))) 2) (sqrt 2)))
175.0ms	(/ (/ (* (cos th) (* (cos th) (cos th))) 2) (sqrt 2))

simplify1.3s

Counts

241 → 241

Iterations

Iter	Nodes
done	2000
2	2000
1	832
0	351

prune1.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes482.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample9.6s

Algorithm

intervals

Results

4.6s	2595×	body	1280	valid
1.9s	1996×	body	640	valid
1.7s	8122×	body	80	valid
727.0ms	1010×	body	320	valid
217.0ms	547×	body	160	valid