Details

sample474.0ms

Algorithm

intervals

Results

144.0ms	55×	body	1280	valid
143.0ms	24×	body	2560	valid
42.0ms	33×	body	640	valid
31.0ms	134×	body	80	valid
13.0ms	16×	body	320	valid
5.0ms	9×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
11	939
10	939
9	887
8	713
7	493
6	401
5	274
4	144
3	85
2	41
1	18
0	10

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(/ (tan (* PI l)) F)
31.3b	(tan (* PI l))

rewrite40.0ms

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:

6.0ms	(* PI l)
7.0ms	(* PI l)
14.0ms	(/ (tan (* PI l)) F)
11.0ms	(tan (* PI l))

series286.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* PI l)
25.0ms	(* PI l)
110.0ms	(/ (tan (* PI l)) F)
119.0ms	(tan (* PI l))

simplify2.2s

Counts

88 → 88

Iterations

Iter	Nodes
4	4316
3	1431
2	533
1	211
0	108

prune993.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.3b	(* (tan (* PI l)) (/ 1 F))
31.3b	(tan (* PI l))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
19×	`associate-r`
17×	`*-un-lft-identity` `add-exp-log`
16×	`add-cube-cbrt`
13×	`add-cbrt-cube`
11×	`times-frac`
10×	`pow1`
9×	`associate-l`
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/` `un-div-inv` `div-inv`

Counts

4 → 86

Calls

4 calls:

7.0ms	(* PI l)
12.0ms	(* PI l)
39.0ms	(* (tan (* PI l)) (/ 1 F))
14.0ms	(tan (* PI l))

series298.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* PI l)
23.0ms	(* PI l)
154.0ms	(* (tan (* PI l)) (/ 1 F))
92.0ms	(tan (* PI l))

simplify1.5s

Counts

98 → 98

Iterations

Iter	Nodes
3	2228
2	839
1	309
0	135

prune1.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.2b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite77.0ms

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×	`insert-posit16` `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 → 59

Calls

4 calls:

34.0ms	(* (sqrt PI) (* (sqrt PI) l))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
40.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series163.0ms

Counts

4 → 8

Calls

4 calls:

46.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
117.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.6s

Counts

67 → 67

Iterations

Iter	Nodes
4	3579
3	1189
2	418
1	153
0	73

prune953.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.8b

localize38.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.6b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`tan-quot`

Counts

4 → 51

Calls

4 calls:

2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
77.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

series129.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
129.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

simplify5.0s

Counts

57 → 57

Iterations

Iter	Nodes
5	7623
4	1696
3	574
2	222
1	92
0	51

prune775.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 9.8b

regimes631.0ms

Accuracy

44.6% (2.3b remaining)

Error of 10.6b against oracle of 8.3b and baseline of 12.5b

bsearch2.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	24

end0.0ms

sample12.5s

Algorithm

intervals

Results

4.9s	803×	body	2560	valid
3.9s	1744×	body	1280	valid
1.6s	4482×	body	80	valid
1.1s	945×	body	640	valid
435.0ms	385×	body	320	valid
174.0ms	6×	body	10240	exit
150.0ms	222×	body	160	valid