Details

sample644.0ms

Algorithm

intervals

Results

141.0ms	25×	body	2560	valid
140.0ms	61×	body	1280	valid
127.0ms	31×	body	640	valid
98.0ms	2×	body	10240	exit
33.0ms	139×	body	80	valid
9.0ms	12×	body	320	valid
2.0ms	5×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2002
7	2002
6	817
5	388
4	156
3	86
2	43
1	20
0	10

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.9b

localize35.0ms

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))

rewrite34.0ms

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×	`insert-posit16` `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 → 70

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(* PI l)
13.0ms	(/ (tan (* PI l)) (* F F))
9.0ms	(tan (* PI l))

series356.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* PI l)
22.0ms	(* PI l)
188.0ms	(/ (tan (* PI l)) (* F F))
109.0ms	(tan (* PI l))

simplify921.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	2000
3	2000
2	709
1	230
0	102

prune425.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.8b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

10.0ms	(/ (tan (* PI l)) F)
5.0ms	(* PI l)
12.0ms	(* PI l)
16.0ms	(tan (* PI l))

series378.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (tan (* PI l)) F)
40.0ms	(* PI l)
38.0ms	(* PI l)
117.0ms	(tan (* PI l))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	2029
4	2029
3	1729
2	583
1	221
0	108

prune390.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.7b	(/ 1 (/ F (tan (* PI l))))
31.5b	(tan (* PI l))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
55×	`add-sqr-sqrt`
51×	`*-un-lft-identity` `add-cube-cbrt`
19×	`add-exp-log`
14×	`associate-/r*`
13×	`add-cbrt-cube`
9×	`pow1`
7×	`div-exp`
6×	`associate-r` `associate-l`
5×	`tan-quot` `associate-/r/` `div-inv`
4×	`insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 128

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(* PI l)
14.0ms	(/ 1 (/ F (tan (* PI l))))
14.0ms	(tan (* PI l))

series310.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(* PI l)
23.0ms	(* PI l)
178.0ms	(/ 1 (/ F (tan (* PI l))))
77.0ms	(tan (* PI l))

simplify1.1s

Counts

140 → 140

Iterations

Iter	Nodes
done	2006
3	2006
2	1085
1	464
0	201

prune499.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`associate-l`
17×	`*-un-lft-identity` `add-exp-log`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1`
9×	`associate-r`
6×	`prod-exp`
5×	`unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`pow-prod-down` `tan-quot` `*-commutative`
2×	`div-exp`
1×	`frac-times` `cbrt-undiv` `rec-exp` `1-exp` `associate-l/` `associate-r/` `div-inv`

Counts

4 → 85

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(* PI l)
50.0ms	(* (/ 1 F) (tan (* PI l)))
21.0ms	(tan (* PI l))

series381.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* PI l)
38.0ms	(* PI l)
200.0ms	(* (/ 1 F) (tan (* PI l)))
114.0ms	(tan (* PI l))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	2004
4	2004
3	1980
2	768
1	290
0	127

prune367.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.0b

regimes634.0ms

Accuracy

69% (1.8b remaining)

Error of 8.3b against oracle of 6.5b and baseline of 12.4b

bsearch4.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	29

end0.0ms

sample11.9s

Algorithm

intervals

Results

4.7s	837×	body	2560	valid
4.1s	1646×	body	1280	valid
1.2s	932×	body	640	valid
991.0ms	4495×	body	80	valid
348.0ms	440×	body	320	valid
235.0ms	6×	body	10240	exit
139.0ms	227×	body	160	valid