Details

sample166.0ms

Algorithm

intervals

Results

68.0ms	77×	body	1280	valid
33.0ms	263×	body	80	valid
32.0ms	57×	body	640	valid
13.0ms	31×	body	320	valid
5.0ms	19×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (cos th) (sqrt 2)) (* a1 a1))
0.5b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))
0.7b	(/ (cos th) (sqrt 2))

rewrite92.0ms

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` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `associate-l/` `-commutative`

Counts

4 → 176

Calls

4 calls:

19.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
39.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
16.0ms	(/ (cos th) (sqrt 2))
16.0ms	(/ (cos th) (sqrt 2))

series428.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
138.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
71.0ms	(/ (cos th) (sqrt 2))
81.0ms	(/ (cos th) (sqrt 2))

simplify4.4s

Counts

188 → 188

Iterations

Iter	Nodes
3	7315
2	1785
1	530
0	186

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
47×	`add-sqr-sqrt`
40×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
31×	`sqrt-prod`
25×	`associate-l`
12×	`associate-/r*`
11×	`pow1` `associate-r` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-l/` `associate-r/`

Counts

4 → 149

Calls

4 calls:

13.0ms	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
23.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
20.0ms	(/ (* a2 (cos th)) (sqrt 2))
12.0ms	(/ (cos th) (sqrt 2))

series500.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* a2 (/ (* a2 (cos th)) (sqrt 2)))
171.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
127.0ms	(/ (* a2 (cos th)) (sqrt 2))
76.0ms	(/ (cos th) (sqrt 2))

simplify4.2s

Counts

161 → 161

Iterations

Iter	Nodes
3	7706
2	1822
1	557
0	214

prune2.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos th) (* a1 a1))
0.3b	(/ (* (cos th) (* a1 a1)) (sqrt 2))
0.5b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.7b	(/ (cos th) (sqrt 2))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

44×	`times-frac`
43×	`add-sqr-sqrt`
37×	`*-un-lft-identity` `add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
28×	`sqrt-prod`
25×	`associate-l`
14×	`pow1`
12×	`associate-/r*` `prod-exp` `cbrt-unprod`
6×	`cbrt-undiv` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`associate-*l/`

Counts

4 → 140

Calls

4 calls:

14.0ms	(* (cos th) (* a1 a1))
19.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
45.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
15.0ms	(/ (cos th) (sqrt 2))

series462.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (cos th) (* a1 a1))
178.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))
139.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
78.0ms	(/ (cos th) (sqrt 2))

simplify5.0s

Counts

152 → 152

Iterations

Iter	Nodes
3	8836
2	1817
1	528
0	198

prune2.2s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (/ (cos th) (sqrt 2)) (* a2 a2))
0.6b	(/ (cos th) (sqrt (sqrt 2)))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.7b	(/ (cos th) (sqrt 2))

rewrite109.0ms

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` `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 → 477

Calls

4 calls:

34.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
16.0ms	(/ (cos th) (sqrt (sqrt 2)))
32.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
16.0ms	(/ (cos th) (sqrt 2))

series420.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
105.0ms	(/ (cos th) (sqrt (sqrt 2)))
99.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
76.0ms	(/ (cos th) (sqrt 2))

simplify1.2s

Counts

489 → 489

Iterations

Iter	Nodes
2	2846
1	1120
0	484

prune7.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes422.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	17
1	17
0	13

end0.0ms

sample8.6s

Algorithm

intervals

Results

2.9s	2487×	body	1280	valid
2.3s	2128×	body	640	valid
2.0s	7966×	body	80	valid
609.0ms	1040×	body	320	valid
284.0ms	495×	body	160	valid