Details

sample278.0ms

Algorithm

intervals

Results

83.0ms	269×	body	80	valid
75.0ms	69×	body	1280	valid
64.0ms	76×	body	640	valid
23.0ms	38×	body	320	valid
4.0ms	10×	body	160	valid

simplify179.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	134
7	134
6	122
5	110
4	98
3	80
2	55
1	26
0	12

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

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))

rewrite130.0ms

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:

46.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
43.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
18.0ms	(/ (cos th) (sqrt 2))
18.0ms	(/ (cos th) (sqrt 2))

series423.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
149.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
75.0ms	(/ (cos th) (sqrt 2))
62.0ms	(/ (cos th) (sqrt 2))

simplify3.8s

Counts

192 → 192

Iterations

Iter	Nodes
3	7183
2	1739
1	518
0	189

prune2.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

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×	`expm1-log1p-u` `pow-prod-down` `insert-posit16` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 155

Calls

4 calls:

26.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
9.0ms	(/ (* a2 a2) (sqrt 2))
37.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
18.0ms	(/ (cos th) (sqrt 2))

series539.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
117.0ms	(/ (* a2 a2) (sqrt 2))
153.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
101.0ms	(/ (cos th) (sqrt 2))

simplify3.1s

Counts

167 → 167

Iterations

Iter	Nodes
3	7287
2	1817
1	543
0	213

prune2.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
59×	`add-sqr-sqrt`
53×	`*-un-lft-identity` `add-cube-cbrt`
40×	`sqrt-prod`
32×	`add-cbrt-cube` `add-exp-log`
31×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
10×	`associate-r`
8×	`associate-/l*`
7×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `unswap-sqr`
1×	`pow-prod-down` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 174

Calls

4 calls:

35.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
9.0ms	(/ (sqrt 2) (cos th))
17.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
14.0ms	(/ (* a2 a2) (sqrt 2))

series513.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (cos th) (/ (* a2 a2) (sqrt 2)))
74.0ms	(/ (sqrt 2) (cos th))
139.0ms	(/ (* a1 a1) (/ (sqrt 2) (cos th)))
116.0ms	(/ (* a2 a2) (sqrt 2))

simplify732.0ms

Counts

186 → 186

Iterations

Iter	Nodes
2	2236
1	634
0	251

prune2.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

383×	`times-frac`
176×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
132×	`cbrt-prod`
72×	`sqrt-prod`
64×	`add-exp-log`
46×	`add-cbrt-cube`
42×	`div-inv`
41×	`associate-/r*`
30×	`cbrt-undiv` `div-exp`
16×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `associate-/l/`

Counts

4 → 334

Calls

4 calls:

5.0ms	(/ (cbrt (sqrt 2)) (cos th))
23.0ms	(/ (/ (* a1 a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cos th)))
18.0ms	(/ (* a1 a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
20.0ms	(/ (* a2 a2) (sqrt 2))

series1.1s

Counts

4 → 12

Calls

4 calls:

376.0ms	(/ (cbrt (sqrt 2)) (cos th))
144.0ms	(/ (/ (* a1 a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (/ (cbrt (sqrt 2)) (cos th)))
555.0ms	(/ (* a1 a1) (* (cbrt (sqrt 2)) (cbrt (sqrt 2))))
70.0ms	(/ (* a2 a2) (sqrt 2))

simplify2.1s

Counts

346 → 346

Iterations

Iter	Nodes
2	5697
1	1514
0	486

prune5.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

regimes425.0ms

Accuracy

0% (0.5b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample9.6s

Algorithm

intervals

Results

3.0s	2546×	body	1280	valid
2.9s	2111×	body	640	valid
2.3s	7993×	body	80	valid
645.0ms	1030×	body	320	valid
242.0ms	523×	body	160	valid