Details

sample246.0ms

Algorithm

intervals

Results

80.0ms	71×	body	1280	valid
70.0ms	267×	body	80	valid
49.0ms	63×	body	640	valid
14.0ms	26×	body	320	valid
8.0ms	22×	body	160	valid

simplify136.0ms

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: 0.3b

localize50.0ms

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))

rewrite87.0ms

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:

34.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
22.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
9.0ms	(/ (cos th) (sqrt 2))
17.0ms	(/ (cos th) (sqrt 2))

series503.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
153.0ms	(* (/ (cos th) (sqrt 2)) (* a2 a2))
72.0ms	(/ (cos th) (sqrt 2))
103.0ms	(/ (cos th) (sqrt 2))

simplify3.3s

Counts

192 → 192

Iterations

Iter	Nodes
3	7183
2	1739
1	518
0	189

prune2.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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` `insert-posit16` `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 → 144

Calls

4 calls:

15.0ms	(* (cos th) (* a2 a2))
25.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
27.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
15.0ms	(/ (cos th) (sqrt 2))

series389.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (cos th) (* a2 a2))
117.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
142.0ms	(* (/ (cos th) (sqrt 2)) (* a1 a1))
81.0ms	(/ (cos th) (sqrt 2))

simplify4.3s

Counts

156 → 156

Iterations

Iter	Nodes
3	8833
2	1810
1	525
0	202

prune1.9s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

33.0ms	(* (cos th) (* a2 a2))
26.0ms	(* (cos th) (* a1 a1))
23.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
41.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))

series464.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos th) (* a2 a2))
55.0ms	(* (cos th) (* a1 a1))
161.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
176.0ms	(/ (* (cos th) (* a1 a1)) (sqrt 2))

simplify4.6s

Counts

120 → 120

Iterations

Iter	Nodes
3	10631
2	1665
1	448
0	164

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (cos th) (* a2 a2)) (sqrt 2))
0.3b	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
0.6b	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
0.6b	(/ (cos th) (sqrt (sqrt 2)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

1143×	`sqrt-prod`
1125×	`times-frac`
615×	`add-sqr-sqrt`
581×	`*-un-lft-identity` `add-cube-cbrt`
283×	`associate-l`
41×	`add-cbrt-cube` `add-exp-log`
35×	`associate-/l*`
24×	`associate-/r*`
23×	`div-inv`
13×	`cbrt-undiv` `div-exp` `unswap-sqr`
12×	`prod-exp` `cbrt-unprod`
9×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down`
1×	`associate-r` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 746

Calls

4 calls:

21.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
45.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
23.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
9.0ms	(/ (cos th) (sqrt (sqrt 2)))

series511.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(/ (* (cos th) (* a2 a2)) (sqrt 2))
135.0ms	(* (/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* a1 a1))
84.0ms	(/ (/ (cos th) (sqrt (sqrt 2))) (sqrt (sqrt 2)))
142.0ms	(/ (cos th) (sqrt (sqrt 2)))

simplify2.5s

Counts

758 → 758

Iterations

Iter	Nodes
2	5720
1	1725
0	595

prune11.9s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes353.0ms

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
2	25
1	25
0	19

end0.0ms

sample8.1s

Algorithm

intervals

Results

2.9s	2442×	body	1280	valid
2.6s	2085×	body	640	valid
1.4s	8032×	body	80	valid
585.0ms	1061×	body	320	valid
213.0ms	516×	body	160	valid