Details

sample472.0ms

Algorithm

intervals

Results

81.0ms	25×	body	2560	valid
35.0ms	49×	body	1280	valid
31.0ms	27×	body	640	valid
12.0ms	161×	body	80	valid
3.0ms	13×	body	320	valid
1.0ms	5×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	14
1	18	14
2	39	14
3	76	14
4	114	14
5	136	14
6	142	14
done	142	14

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.5b	(/ 1.0 (* F F))
4.1b	(* (/ 1.0 (* F F)) (tan (* PI l)))
27.7b	(tan (* PI l))

rewrite79.0ms

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` `div-exp` `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 → 77

Calls

4 calls:

9.0ms	(* PI l)
8.0ms	(/ 1.0 (* F F))
45.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
13.0ms	(tan (* PI l))

series255.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* PI l)
25.0ms	(/ 1.0 (* F F))
137.0ms	(* (/ 1.0 (* F F)) (tan (* PI l)))
72.0ms	(tan (* PI l))

simplify1.9s

Counts

89 → 89

Iterations

Useful iterations: 2 (159.0ms)

Iter	Nodes	Cost
0	135	872
1	305	854
2	1001	722
3	3970	722
done	5001	722

prune215.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 10.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* PI l)
0.2b	(* PI l)
0.3b	(* (/ 1.0 F) (tan (* PI l)))
27.7b	(tan (* PI l))

rewrite60.0ms

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×	`prod-exp` `cbrt-unprod` `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 → 78

Calls

4 calls:

7.0ms	(* PI l)
9.0ms	(* PI l)
34.0ms	(* (/ 1.0 F) (tan (* PI l)))
8.0ms	(tan (* PI l))

series227.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(* PI l)
20.0ms	(* PI l)
126.0ms	(* (/ 1.0 F) (tan (* PI l)))
61.0ms	(tan (* PI l))

simplify1.6s

Counts

90 → 90

Iterations

Useful iterations: 2 (117.0ms)

Iter	Nodes	Cost
0	125	736
1	277	717
2	769	639
3	2333	639
done	5000	639

prune242.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sqrt PI) (* (sqrt PI) l))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
27.5b	(tan (* (sqrt PI) (* (sqrt PI) l)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

27.0ms	(* (sqrt PI) (* (sqrt PI) l))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
25.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

series87.0ms

Counts

4 → 8

Calls

4 calls:

24.0ms	(* (sqrt PI) (* (sqrt PI) l))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
63.0ms	(tan (* (sqrt PI) (* (sqrt PI) l)))

simplify2.8s

Counts

63 → 63

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	70	478
1	151	321
2	418	287
3	1099	287
4	3880	287
done	5001	287

prune190.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.5b

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
27.6b	(tan (* (sqrt PI) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) l)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 47

Calls

4 calls:

1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)
68.0ms	(tan (* (sqrt PI) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) l)))

series69.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
69.0ms	(tan (* (sqrt PI) (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) l)))

simplify1.4s

Counts

53 → 53

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	49	381
1	90	243
2	204	235
3	562	235
4	2268	235
done	5000	233

prune157.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 10.5b

regimes331.0ms

Accuracy

0% (0.3b remaining)

Error of 12.8b against oracle of 12.5b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	30
1	24	30
done	24	30

end0.0ms

sample4.8s

Algorithm

intervals

Results

2.6s	835×	body	2560	valid
1.2s	1657×	body	1280	valid
338.0ms	934×	body	640	valid
303.0ms	4545×	body	80	valid
92.0ms	422×	body	320	valid
32.0ms	209×	body	160	valid
23.0ms	1×	body	10240	exit