Details

sample751.0ms

Algorithm

intervals

Results

412.0ms	31×	body	640	valid
138.0ms	30×	body	2560	valid
67.0ms	56×	body	1280	valid
20.0ms	143×	body	80	valid
3.0ms	10×	body	160	valid
2.0ms	4×	body	320	valid

simplify131.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	148
6	148
5	141
4	118
3	76
2	39
1	18
0	10

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* PI l)
0.3b	(* PI l)
2.7b	(/ (tan (* PI l)) (/ (* F F) 1.0))
30.4b	(tan (* PI l))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

5.0ms	(* PI l)
5.0ms	(* PI l)
15.0ms	(/ (tan (* PI l)) (/ (* F F) 1.0))
14.0ms	(tan (* PI l))

series386.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* PI l)
45.0ms	(* PI l)
204.0ms	(/ (tan (* PI l)) (/ (* F F) 1.0))
100.0ms	(tan (* PI l))

simplify1.1s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	2520
1	445
0	168

prune700.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 15.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (tan (* PI l)) F)
0.3b	(* PI l)
0.3b	(* PI l)
30.4b	(tan (* PI l))

rewrite58.0ms

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×	`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 → 72

Calls

4 calls:

22.0ms	(/ (tan (* PI l)) F)
11.0ms	(* PI l)
11.0ms	(* PI l)
12.0ms	(tan (* PI l))

series277.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(/ (tan (* PI l)) F)
35.0ms	(* PI l)
28.0ms	(* PI l)
79.0ms	(tan (* PI l))

simplify1.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
3	3500
2	679
1	217
0	105

prune489.0ms

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 PI) (* l (sqrt PI)))
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.4b	(tan (* (sqrt PI) (* l (sqrt PI))))

rewrite81.0ms

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×	`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 → 55

Calls

4 calls:

44.0ms	(* (sqrt PI) (* l (sqrt PI)))
2.0ms	(sqrt PI)
2.0ms	(sqrt PI)
31.0ms	(tan (* (sqrt PI) (* l (sqrt PI))))

series176.0ms

Counts

4 → 8

Calls

4 calls:

51.0ms	(* (sqrt PI) (* l (sqrt PI)))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
124.0ms	(tan (* (sqrt PI) (* l (sqrt PI))))

simplify1.5s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
3	3036
2	590
1	172
0	78

prune555.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 15.0b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b	(sqrt PI)
1.0b	(sqrt PI)
1.0b	(sqrt PI)
30.8b	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* l (sqrt PI))))

rewrite51.0ms

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` `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)
2.0ms	(sqrt PI)
46.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* l (sqrt PI))))

series116.0ms

Counts

4 → 6

Calls

4 calls:

0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)
116.0ms	(tan (* (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (* l (sqrt PI))))

simplify839.0ms

Counts

53 → 53

Iterations

Iter	Nodes
done	5000
3	1094
2	257
1	97
0	49

prune405.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 15.0b

regimes656.0ms

Accuracy

0% (0.3b remaining)

Error of 12.7b against oracle of 12.4b and baseline of 12.7b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	17

end0.0ms

sample10.0s

Algorithm

intervals

Results

5.2s	871×	body	2560	valid
2.6s	1652×	body	1280	valid
783.0ms	976×	body	640	valid
667.0ms	4502×	body	80	valid
258.0ms	378×	body	320	valid
105.0ms	3×	body	10240	exit
67.0ms	218×	body	160	valid