Details

sample446.0ms

Algorithm

intervals

Results

146.0ms	59×	body	1280	valid
144.0ms	57×	body	640	valid
73.0ms	190×	body	80	valid
39.0ms	30×	body	320	valid
12.0ms	14×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

Iter	Nodes
4	6637
3	1079
2	183
1	52
0	19

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ l t) (/ l t))
1.8b	(* (/ t (* (/ l t) (/ l t))) (sin k))
2.4b	(/ t (* (/ l t) (/ l t)))
14.4b	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-cbrt-cube` `add-exp-log`
70×	`cbrt-undiv` `div-exp`
61×	`times-frac`
57×	`add-sqr-sqrt`
46×	`prod-exp` `cbrt-unprod`
41×	`*-un-lft-identity` `add-cube-cbrt`
23×	`associate-l`
16×	`associate-r`
13×	`pow1` `swap-sqr`
11×	`associate-/l*`
9×	`associate-/r/` `div-inv`
7×	`associate-*l/`
6×	`unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`frac-times` `associate-*r/`
2×	`clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `-commutative`
1×	`pow2` `pow-plus` `tan-quot` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 207

Calls

4 calls:

18.0ms	(* (/ l t) (/ l t))
44.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
10.0ms	(/ t (* (/ l t) (/ l t)))
63.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

series600.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ l t) (/ l t))
137.0ms	(* (/ t (* (/ l t) (/ l t))) (sin k))
69.0ms	(/ t (* (/ l t) (/ l t)))
349.0ms	(/ (/ 2 (* (/ t (* (/ l t) (/ l t))) (sin k))) (* (tan k) (fma (/ k t) (/ k t) 2)))

simplify1.4s

Counts

219 → 219

Iterations

Iter	Nodes
2	4126
1	1060
0	343

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 11.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ l t) (/ l t))
0.3b	(/ 2 (* t (sin k)))
3.7b	(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
11.9b	(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

254×	`add-cbrt-cube` `add-exp-log`
135×	`times-frac`
133×	`cbrt-undiv` `div-exp`
72×	`add-sqr-sqrt`
68×	`prod-exp` `cbrt-unprod`
60×	`*-un-lft-identity` `add-cube-cbrt`
28×	`associate-/r/`
24×	`div-inv`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1` `associate-l/` `associate-/l`
10×	`frac-times` `associate-/r` `associate-r/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`pow2` `pow-plus` `pow-prod-down` `tan-quot` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 286

Calls

4 calls:

19.0ms	(* (/ l t) (/ l t))
7.0ms	(/ 2 (* t (sin k)))
31.0ms	(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
38.0ms	(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

series785.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (/ l t) (/ l t))
62.0ms	(/ 2 (* t (sin k)))
468.0ms	(/ (/ 2 (* t (sin k))) (/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t))))
227.0ms	(/ (* (tan k) (fma (/ k t) (/ k t) 2)) (* (/ l t) (/ l t)))

simplify2.0s

Counts

298 → 298

Iterations

Iter	Nodes
2	5990
1	1392
0	452

prune2.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ t l) (/ t l))
1.3b	(* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))
3.5b	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
3.7b	(/ (/ 2 (* t (sin k))) (fma 2 (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) (* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-cbrt-cube` `add-exp-log`
93×	`times-frac`
80×	`add-sqr-sqrt`
62×	`*-un-lft-identity` `add-cube-cbrt`
41×	`prod-exp` `cbrt-unprod`
39×	`associate-l`
35×	`cbrt-undiv` `div-exp`
21×	`pow1`
15×	`associate-r`
13×	`swap-sqr`
11×	`frac-times` `associate-*r/` `div-inv`
8×	`unswap-sqr`
7×	`pow-prod-down` `associate-l/` `associate-/l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 233

Calls

4 calls:

21.0ms	(* (/ t l) (/ t l))
34.0ms	(* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))
47.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
30.0ms	(/ (/ 2 (* t (sin k))) (fma 2 (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) (* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))))

series938.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (/ t l) (/ t l))
94.0ms	(* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))
174.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
629.0ms	(/ (/ 2 (* t (sin k))) (fma 2 (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) (* (/ (sin k) (cos k)) (* (/ k l) (/ k l)))))

simplify1.7s

Counts

245 → 245

Iterations

Iter	Nodes
2	4718
1	1289
0	420

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ t l) (/ t l))
0.3b	(* (/ (sin k) (cos k)) (/ k l))
3.5b	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
3.7b	(/ (/ 2 (* t (sin k))) (fma 2 (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) (* (* (/ (sin k) (cos k)) (/ k l)) (/ k l))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

105×	`times-frac`
96×	`add-sqr-sqrt`
78×	`add-cbrt-cube` `add-exp-log`
69×	`*-un-lft-identity` `add-cube-cbrt`
39×	`associate-l`
27×	`associate-r` `prod-exp` `cbrt-unprod`
26×	`cbrt-undiv` `div-exp`
18×	`pow1`
13×	`swap-sqr`
12×	`div-inv`
10×	`unswap-sqr`
7×	`frac-times` `associate-r/` `associate-/l`
5×	`pow-prod-down` `associate-*l/`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative`
1×	`pow2` `clear-num` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 230

Calls

4 calls:

28.0ms	(* (/ t l) (/ t l))
21.0ms	(* (/ (sin k) (cos k)) (/ k l))
43.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
37.0ms	(/ (/ 2 (* t (sin k))) (fma 2 (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) (* (* (/ (sin k) (cos k)) (/ k l)) (/ k l))))

series909.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ t l) (/ t l))
110.0ms	(* (/ (sin k) (cos k)) (/ k l))
129.0ms	(* (/ (sin k) (cos k)) (* (/ t l) (/ t l)))
641.0ms	(/ (/ 2 (* t (sin k))) (fma 2 (* (/ (sin k) (cos k)) (* (/ t l) (/ t l))) (* (* (/ (sin k) (cos k)) (/ k l)) (/ k l))))

simplify1.6s

Counts

242 → 242

Iterations

Iter	Nodes
2	4644
1	1276
0	420

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 2.6b

regimes427.0ms

Accuracy

71.6% (1.4b remaining)

Error of 4.7b against oracle of 3.3b and baseline of 8.2b

bsearch355.0ms

Steps

Iters	Range		Point
8	7.405009204228503e-65	4.7093230820561426e-62	6.996202509808683e-64
8	-2.9534264795978874e-95	-9.53134385382187e-100	-1.2768326759006626e-98

simplify17.0ms

Iterations

Iter	Nodes
2	47
1	47
0	43

end0.0ms

sample15.2s

Algorithm

intervals

Results

6.7s	1983×	body	1280	valid
3.7s	1723×	body	640	valid
2.6s	5912×	body	80	valid
1.2s	848×	body	320	valid
437.0ms	437×	body	160	valid