Details

sample511.0ms

Algorithm

intervals

Results

104.0ms	32×	body	2560	valid
45.0ms	58×	body	1280	valid
29.0ms	142×	body	80	valid
9.0ms	28×	body	640	valid
3.0ms	15×	body	320	valid
0.0ms	1×	body	160	valid

simplify21.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	19	7
1	41	7
2	82	7
3	122	7
4	147	7
5	157	7
6	159	7
7	159	7
done	159	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.4b	(/ 1.0 (* F F))
3.9b	(* (/ 1.0 (* F F)) (tan (* PI l)))
31.1b	(tan (* PI l))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
17×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-l`
8×	`pow1`
7×	`times-frac`
6×	`associate-r` `prod-exp` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `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` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r*`

Counts

4 → 85

Calls

4 calls:

6.0ms	(* PI l)
7.0ms	(/ 1.0 (* F F))
48.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
9.0ms	(tan (* PI l))

series261.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* PI l)
26.0ms	(/ 1.0 (* F F))
134.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
78.0ms	(tan (* PI l))

simplify42.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	334	468
1	1442	399
2	5001	398
done	5001	398

prune241.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
31.1b	(tan (* PI l))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

6.0ms	(* PI l)
7.0ms	(* PI l)
33.0ms	(* (/ 1.0 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series234.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
24.0ms	(* PI l)
125.0ms	(* (/ 1.0 F) (tan (* PI l)))
65.0ms	(tan (* PI l))

simplify87.0ms

Counts

98 → 98

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	286	403
1	1032	363
2	3928	361
3	5001	360
done	5001	360

prune283.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) l)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.0b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 64

Calls

4 calls:

9.0ms	(* (sqrt PI) l)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
24.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series118.0ms

Counts

4 → 8

Calls

4 calls:

55.0ms	(* (sqrt PI) l)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
63.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify47.0ms

Counts

72 → 72

Iterations

Useful iterations: 2 (13.0ms)

Iter	Nodes	Cost
0	136	250
1	437	236
2	1306	234
3	5001	234
done	5001	234

prune257.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 15.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
31.0b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

2.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
44.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

series70.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
70.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* (sqrt PI) l)))

simplify38.0ms

Counts

61 → 61

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	95	251
1	264	232
2	946	232
3	5001	232
done	5001	232

prune236.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 15.4b

regimes392.0ms

Accuracy

0% (0.3b remaining)

Error of 12.5b against oracle of 12.2b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19
done	24	19

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	847×	body	2560	valid
1.2s	1729×	body	1280	valid
300.0ms	877×	body	640	valid
275.0ms	4493×	body	80	valid
93.0ms	443×	body	320	valid
70.0ms	3×	body	10240	exit
36.0ms	208×	body	160	valid