Details

sample443.0ms

Algorithm

intervals

Results

116.0ms	22×	body	2560	valid
102.0ms	58×	body	1280	valid
20.0ms	150×	body	80	valid
18.0ms	25×	body	640	valid
11.0ms	19×	body	320	valid
2.0ms	8×	body	160	valid

simplify486.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	142
7	142
6	139
5	125
4	109
3	70
2	41
1	19
0	10

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.6b	(/ 1.0 (* F F))
4.4b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.2b	(tan (* PI l))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

6.0ms	(* PI l)
7.0ms	(/ 1.0 (* F F))
71.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
50.0ms	(tan (* PI l))

series320.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
32.0ms	(/ 1.0 (* F F))
166.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
99.0ms	(tan (* PI l))

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5001
2	1224
1	343
0	143

prune580.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
0.3b	(* PI l)
0.3b	(* PI l)
30.2b	(tan (* PI l))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
28×	`associate-l`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
13×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `sqrt-prod`
9×	`associate-r`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `tan-quot` `*-commutative`
1×	`frac-times` `cbrt-undiv` `div-exp` `associate-l/` `associate-r/` `div-inv`

Counts

4 → 96

Calls

4 calls:

44.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
5.0ms	(* PI l)
6.0ms	(* PI l)
15.0ms	(tan (* PI l))

series446.0ms

Counts

4 → 12

Calls

4 calls:

260.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
44.0ms	(* PI l)
39.0ms	(* PI l)
103.0ms	(tan (* PI l))

simplify2.3s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
3	2808
2	906
1	315
0	138

prune746.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.2b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-r` `tan-quot` `*-commutative`

Counts

4 → 63

Calls

4 calls:

41.0ms	(* (sqrt PI) (* (sqrt PI) l))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
38.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series130.0ms

Counts

4 → 8

Calls

4 calls:

37.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
93.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify3.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5107
4	3032
3	1160
2	448
1	162
0	76

prune485.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.4b

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.3b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`tan-quot`

Counts

4 → 55

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
50.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

series120.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
120.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

simplify2.1s

Counts

61 → 61

Iterations

Iter	Nodes
done	5001
4	2028
3	721
2	246
1	103
0	53

prune496.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.4b

regimes984.0ms

Accuracy

0% (0.3b remaining)

Error of 12.4b against oracle of 12.1b and baseline of 12.4b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	21
1	21
0	16

end0.0ms

sample9.4s

Algorithm

intervals

Results

4.3s	793×	body	2560	valid
2.8s	1709×	body	1280	valid
806.0ms	968×	body	640	valid
696.0ms	4498×	body	80	valid
315.0ms	9×	body	10240	exit
168.0ms	398×	body	320	valid
59.0ms	209×	body	160	valid