Details

sample468.0ms

Algorithm

intervals

Results

128.0ms	61×	body	1280	valid
117.0ms	25×	body	2560	valid
65.0ms	2×	body	10240	exit
38.0ms	31×	body	640	valid
30.0ms	139×	body	80	valid
7.0ms	12×	body	320	valid
2.0ms	5×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2001
7	2001
6	880
5	396
4	166
3	91
2	45
1	21
0	10

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
4.5b	(/ (tan (* PI l)) (* F F))
31.5b	(tan (* PI l))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `tan-quot` `*-commutative` `unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv` `associate-/l/`

Counts

4 → 78

Calls

4 calls:

11.0ms	(* PI l)
11.0ms	(* PI l)
28.0ms	(/ (tan (* PI l)) (* F F))
19.0ms	(tan (* PI l))

series380.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* PI l)
41.0ms	(* PI l)
200.0ms	(/ (tan (* PI l)) (* F F))
107.0ms	(tan (* PI l))

simplify913.0ms

Counts

90 → 90

Iterations

Iter	Nodes
done	2014
3	2014
2	719
1	240
0	108

prune470.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
30.8b	(sin (* PI l))
31.1b	(cos (* PI l))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
6×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 62

Calls

4 calls:

10.0ms	(* PI l)
11.0ms	(* PI l)
10.0ms	(sin (* PI l))
12.0ms	(cos (* PI l))

series146.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* PI l)
44.0ms	(* PI l)
43.0ms	(sin (* PI l))
34.0ms	(cos (* PI l))

simplify1.3s

Counts

74 → 74

Iterations

Iter	Nodes
done	2029
4	2029
3	1583
2	456
1	172
0	83

prune449.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.7b

localize50.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
30.8b	(sin (* PI l))
31.1b	(cos (posit16->real (real->posit16 (* PI l))))
60.1b	(posit16->real (real->posit16 (* PI l)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `remove-posit16` `unswap-sqr`

Counts

4 → 52

Calls

4 calls:

5.0ms	(* PI l)
7.0ms	(sin (* PI l))
3.0ms	(cos (posit16->real (real->posit16 (* PI l))))
1.0ms	(posit16->real (real->posit16 (* PI l)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* PI l)
48.0ms	(sin (* PI l))
33.0ms	(cos (posit16->real (real->posit16 (* PI l))))
30.0ms	(posit16->real (real->posit16 (* PI l)))

simplify1.3s

Counts

64 → 64

Iterations

Iter	Nodes
done	2000
4	2000
3	1556
2	486
1	183
0	95

prune634.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.7b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 F) (/ (tan (* PI l)) F))
0.3b	(* PI l)
0.3b	(* PI l)
31.5b	(tan (* PI l))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
30×	`add-exp-log`
25×	`times-frac`
24×	`*-un-lft-identity`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`associate-r` `associate-l`
10×	`pow1` `prod-exp`
8×	`div-exp` `unswap-sqr`
6×	`cbrt-unprod`
4×	`expm1-log1p-u` `cbrt-undiv` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `*-commutative`
2×	`rec-exp` `1-exp` `div-inv`
1×	`frac-times` `associate-l/` `tan-quot` `associate-r/`

Counts

4 → 112

Calls

4 calls:

34.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
11.0ms	(* PI l)
11.0ms	(* PI l)
17.0ms	(tan (* PI l))

series372.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (/ 1 F) (/ (tan (* PI l)) F))
28.0ms	(* PI l)
46.0ms	(* PI l)
92.0ms	(tan (* PI l))

simplify1.2s

Counts

124 → 124

Iterations

Iter	Nodes
done	2005
3	2005
2	1390
1	464
0	171

prune452.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.7b

regimes727.0ms

Accuracy

84.1% (0.7b remaining)

Error of 8.9b against oracle of 8.2b and baseline of 12.6b

bsearch3.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample11.8s

Algorithm

intervals

Results

5.1s	837×	body	2560	valid
3.1s	1646×	body	1280	valid
1.6s	4495×	body	80	valid
1.1s	932×	body	640	valid
350.0ms	440×	body	320	valid
174.0ms	6×	body	10240	exit
104.0ms	227×	body	160	valid