Details

sample323.0ms

Algorithm

intervals

Results

113.0ms	30×	body	2560	valid
52.0ms	56×	body	1280	valid
17.0ms	143×	body	80	valid
15.0ms	31×	body	640	valid
3.0ms	10×	body	160	valid
1.0ms	4×	body	320	valid

simplify201.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	10	299
1	19	299
2	41	299
3	82	299
4	126	299
5	152	299
6	162	299
7	164	299
done	164	299

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.4b	(/ 1.0 (* F F))
3.0b	(* (/ 1.0 (* F F)) (tan (* PI l)))
30.4b	(tan (* PI l))

rewrite77.0ms

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:

11.0ms	(* PI l)
16.0ms	(/ 1.0 (* F F))
35.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
8.0ms	(tan (* PI l))

series401.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* PI l)
44.0ms	(/ 1.0 (* F F))
182.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
136.0ms	(tan (* PI l))

simplify1.5s

Counts

97 → 97

Iterations

Useful iterations: 2 (459.0ms)

Iter	Nodes	Cost
0	143	22953
1	352	20688
2	1985	20247
done	5001	20247

prune589.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 15.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
0.4b	(* (/ (sqrt 1.0) F) (tan (* PI l)))
30.4b	(tan (* PI l))

rewrite87.0ms

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:

11.0ms	(* PI l)
10.0ms	(* PI l)
54.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
6.0ms	(tan (* PI l))

series391.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* PI l)
32.0ms	(* PI l)
217.0ms	(* (/ (sqrt 1.0) F) (tan (* PI l)))
106.0ms	(tan (* PI l))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	138	25810
1	317	24700
2	1296	24659
done	5001	24019

prune646.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 15.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sqrt 1.0) F) (tan (* (sqrt PI) (* (sqrt PI) l))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.4b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
22×	`associate-l`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
16×	`sqrt-prod`
9×	`add-cbrt-cube` `add-exp-log`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `tan-quot` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `prod-exp` `cbrt-unprod`
1×	`frac-times` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `div-inv`

Counts

4 → 86

Calls

4 calls:

81.0ms	(* (/ (sqrt 1.0) F) (tan (* (sqrt PI) (* (sqrt PI) l))))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
44.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series339.0ms

Counts

4 → 8

Calls

4 calls:

211.0ms	(* (/ (sqrt 1.0) F) (tan (* (sqrt PI) (* (sqrt PI) l))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
128.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify1.8s

Counts

94 → 94

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	133	29156
1	294	23226
2	1173	23105
done	5001	22970

prune736.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.0b

localize70.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
29.8b	(sin (* (sqrt PI) (* (sqrt PI) l)))
30.1b	(cos (* (sqrt PI) (* (sqrt PI) l)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 48

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
17.0ms	(sin (* (sqrt PI) (* (sqrt PI) l)))
22.0ms	(cos (* (sqrt PI) (* (sqrt PI) l)))

series84.0ms

Counts

4 → 8

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
49.0ms	(sin (* (sqrt PI) (* (sqrt PI) l)))
35.0ms	(cos (* (sqrt PI) (* (sqrt PI) l)))

simplify3.1s

Counts

56 → 56

Iterations

Useful iterations: 3 (1.0s)

Iter	Nodes	Cost
0	77	11019
1	149	8275
2	528	8079
3	3178	7854
done	5001	7854

prune470.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.8b

regimes839.0ms

Accuracy

85.6% (0.7b remaining)

Error of 8.5b against oracle of 7.8b and baseline of 12.7b

bsearch3.0ms

simplify14.0ms

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	43	1789
1	55	1789
done	55	1789

end0.0ms

sample10.1s

Algorithm

intervals

Results

5.5s	871×	body	2560	valid
2.3s	1652×	body	1280	valid
974.0ms	976×	body	640	valid
734.0ms	4502×	body	80	valid
170.0ms	378×	body	320	valid
90.0ms	3×	body	10240	exit
64.0ms	218×	body	160	valid