Details

sample501.0ms

Algorithm

intervals

Results

168.0ms	28×	body	2560	valid
98.0ms	52×	body	1280	valid
90.0ms	153×	body	80	valid
46.0ms	35×	body	640	valid
8.0ms	10×	body	320	valid
3.0ms	8×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
4.2b	(/ (tan (* PI l)) (* F F))
30.2b	(tan (* PI l))

rewrite41.0ms

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:

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

series361.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* PI l)
39.0ms	(* PI l)
158.0ms	(/ (tan (* PI l)) (* F F))
123.0ms	(tan (* PI l))

simplify969.0ms

Counts

90 → 90

Iterations

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

prune508.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.2b	(* PI l)
0.2b	(* PI l)
30.2b	(tan (* PI l))

rewrite53.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 84

Calls

4 calls:

23.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
10.0ms	(* PI l)
8.0ms	(tan (* PI l))

series287.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (tan (* PI l)) F)
39.0ms	(* PI l)
23.0ms	(* PI l)
87.0ms	(tan (* PI l))

simplify1.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	2029
4	2029
3	1667
2	588
1	227
0	114

prune535.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 7.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.5b	(/ 1 (/ F (tan (* PI l))))
30.2b	(tan (* PI l))

rewrite49.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 136

Calls

4 calls:

8.0ms	(* PI l)
5.0ms	(* PI l)
17.0ms	(/ 1 (/ F (tan (* PI l))))
17.0ms	(tan (* PI l))

series299.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* PI l)
31.0ms	(* PI l)
154.0ms	(/ 1 (/ F (tan (* PI l))))
85.0ms	(tan (* PI l))

simplify964.0ms

Counts

148 → 148

Iterations

Iter	Nodes
done	2003
3	2003
2	1065
1	473
0	207

prune594.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (/ F (tan (* (sqrt PI) (* (sqrt PI) l)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.0b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
51×	`add-sqr-sqrt`
49×	`*-un-lft-identity` `add-cube-cbrt`
15×	`add-exp-log`
14×	`associate-/r*`
9×	`add-cbrt-cube`
7×	`pow1` `div-exp`
6×	`sqrt-prod`
5×	`tan-quot` `associate-/r/` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 126

Calls

4 calls:

65.0ms	(/ 1 (/ F (tan (* (sqrt PI) (* (sqrt PI) l)))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
30.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series278.0ms

Counts

4 → 8

Calls

4 calls:

175.0ms	(/ 1 (/ F (tan (* (sqrt PI) (* (sqrt PI) l)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
103.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify1.0s

Counts

134 → 134

Iterations

Iter	Nodes
done	2005
3	2005
2	1103
1	454
0	199

prune589.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.2b

regimes446.0ms

Accuracy

58% (2.4b remaining)

Error of 8.8b against oracle of 6.4b and baseline of 12.1b

bsearch3.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	28
1	28
0	27

end0.0ms

sample11.9s

Algorithm

intervals

Results

5.0s	821×	body	2560	valid
3.6s	1636×	body	1280	valid
1.3s	4615×	body	80	valid
1.2s	968×	body	640	valid
250.0ms	360×	body	320	valid
186.0ms	6×	body	10240	exit
100.0ms	206×	body	160	valid