Details

sample244.0ms

Algorithm

intervals

Results

124.0ms	68×	body	1280	valid
44.0ms	54×	body	640	valid
28.0ms	160×	body	80	valid
17.0ms	29×	body	320	valid
8.0ms	20×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	1118
2	185
1	54
0	19

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 20.6b

localize39.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* (/ t l) (/ t l)) t)
4.1b	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
4.1b	(* (sin k) (* (* (/ t l) (/ t l)) t))
11.8b	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

rewrite630.0ms

Algorithm

rewrite-expression-head

Rules

209×	`add-cbrt-cube` `add-exp-log`
187×	`times-frac`
84×	`prod-exp` `cbrt-unprod`
81×	`cbrt-undiv` `div-exp`
75×	`add-sqr-sqrt`
74×	`*-un-lft-identity` `add-cube-cbrt`
35×	`associate-/l*`
28×	`associate-*l/`
25×	`associate-*r/`
23×	`associate-/r/`
18×	`pow1`
12×	`div-inv`
9×	`pow-prod-down`
7×	`frac-times`
6×	`tan-quot`
4×	`associate-/r` `associate-r` `associate-l*` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`flip3-+` `flip-+` `unswap-sqr`

Counts

4 → 263

Calls

4 calls:

63.0ms	(* (* (/ t l) (/ t l)) t)
154.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
157.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
239.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

series1.5s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* (/ t l) (/ t l)) t)
358.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
154.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
905.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

simplify1.8s

Counts

275 → 275

Iterations

Iter	Nodes
done	5000
1	1235
0	448

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (/ t l))
2.2b	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
4.0b	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
11.6b	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

rewrite817.0ms

Algorithm

rewrite-expression-head

Rules

278×	`add-cbrt-cube` `add-exp-log`
133×	`prod-exp` `cbrt-unprod`
88×	`cbrt-undiv` `div-exp`
86×	`associate-*l/`
71×	`times-frac`
61×	`frac-times`
59×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
37×	`pow1`
28×	`associate-*r/`
27×	`tan-quot`
23×	`associate-/r/`
19×	`pow-prod-down`
18×	`flip3-+` `flip-+`
17×	`associate-r`
15×	`associate-l`
13×	`swap-sqr` `associate-/l*`
7×	`div-inv`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `pow-plus` `pow-sqr` `pow-prod-up` `associate-/l/`

Counts

4 → 288

Calls

4 calls:

27.0ms	(* (/ t l) (/ t l))
85.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
344.0ms	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
328.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

series1.5s

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (/ t l) (/ t l))
182.0ms	(* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t)
926.0ms	(/ (/ 2 (sin k)) (* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l))))
304.0ms	(* (* (* (+ (* (/ k t) (/ k t)) 2) (tan k)) t) (* (/ t l) (/ t l)))

simplify2.2s

Counts

300 → 300

Iterations

Iter	Nodes
done	5002
1	1526
0	455

prune1.8s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 5.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ t l) (* (/ t l) (sin k)))
1.9b	(* (/ t l) (sin k))
3.7b	(* (* (tan k) t) (* (/ t l) (* (/ t l) (sin k))))
11.5b	(* (+ (* (/ k t) (/ k t)) 2) (* (* (tan k) t) (* (/ t l) (* (/ t l) (sin k)))))

rewrite870.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-cbrt-cube` `add-exp-log`
109×	`prod-exp` `cbrt-unprod`
61×	`pow1`
50×	`associate-*l/`
41×	`pow-prod-down`
35×	`frac-times`
30×	`associate-l`
28×	`associate-*r/`
26×	`cbrt-undiv` `div-exp`
25×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
16×	`tan-quot`
8×	`flip3-+` `flip-+`
6×	`associate-r`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`div-inv` `unswap-sqr`

Counts

4 → 198

Calls

4 calls:

77.0ms	(* (/ t l) (* (/ t l) (sin k)))
27.0ms	(* (/ t l) (sin k))
180.0ms	(* (* (tan k) t) (* (/ t l) (* (/ t l) (sin k))))
575.0ms	(* (+ (* (/ k t) (/ k t)) 2) (* (* (tan k) t) (* (/ t l) (* (/ t l) (sin k)))))

series822.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(* (/ t l) (* (/ t l) (sin k)))
124.0ms	(* (/ t l) (sin k))
261.0ms	(* (* (tan k) t) (* (/ t l) (* (/ t l) (sin k))))
312.0ms	(* (+ (* (/ k t) (/ k t)) 2) (* (* (tan k) t) (* (/ t l) (* (/ t l) (sin k)))))

simplify1.6s

Counts

210 → 210

Iterations

Iter	Nodes
done	5001
1	975
0	311

prune1.3s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.0b

localize80.0ms

Local error

Found 4 expressions with local error:

1.9b	(* (sin k) (/ t l))
1.9b	(* (sin k) (/ t l))
2.2b	(* (* (* (sin k) (/ t l)) (* (sin k) (/ t l))) t)
11.6b	(* (* (* (* (sin k) (/ t l)) (* (sin k) (/ t l))) t) (+ (* (/ k t) (/ k t)) 2))

rewrite1.3s

Algorithm

rewrite-expression-head

Rules

120×	`add-cbrt-cube` `add-exp-log`
77×	`prod-exp` `cbrt-unprod`
51×	`pow1`
34×	`pow-prod-down`
33×	`add-sqr-sqrt`
32×	`associate-r`
24×	`associate-*r/`
22×	`*-un-lft-identity` `add-cube-cbrt`
20×	`times-frac`
19×	`associate-*l/`
14×	`cbrt-undiv` `div-exp`
10×	`frac-times`
8×	`associate-l`
5×	`unswap-sqr`
4×	`flip3-+` `*-commutative` `flip-+` `insert-posit16` `add-log-exp`
2×	`div-inv`
1×	`distribute-rgt-in` `distribute-lft-in`

Counts

4 → 162

Calls

4 calls:

24.0ms	(* (sin k) (/ t l))
16.0ms	(* (sin k) (/ t l))
225.0ms	(* (* (* (sin k) (/ t l)) (* (sin k) (/ t l))) t)
995.0ms	(* (* (* (* (sin k) (/ t l)) (* (sin k) (/ t l))) t) (+ (* (/ k t) (/ k t)) 2))

series529.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin k) (/ t l))
73.0ms	(* (sin k) (/ t l))
164.0ms	(* (* (* (sin k) (/ t l)) (* (sin k) (/ t l))) t)
223.0ms	(* (* (* (* (sin k) (/ t l)) (* (sin k) (/ t l))) t) (+ (* (/ k t) (/ k t)) 2))

simplify2.9s

Counts

174 → 174

Iterations

Iter	Nodes
done	5002
2	4388
1	846
0	251

prune892.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 5.0b

regimes632.0ms

Accuracy

35.9% (6.3b remaining)

Error of 12.4b against oracle of 6.1b and baseline of 16.0b

bsearch1.4s

Steps

Iters	Range		Point
8	3.6124353308741163e+137	3.2407605759015045e+140	8.785675515272592e+137
7	4.916263598749366e-218	1.3400765927422313e-216	7.328736741637738e-217
8	-1.2685277833442503e-121	-9.432483994551924e-125	-1.0539765897933676e-121
6	-5.475978031765872e+141	-5.9028139372446406e+140	-2.5994779280181517e+141

simplify20.0ms

Iterations

Iter	Nodes
done	70
1	70
0	55

end0.0ms

sample10.6s

Algorithm

intervals

Results

4.2s	2057×	body	1280	valid
2.6s	1715×	body	640	valid
2.4s	5938×	body	80	valid
686.0ms	823×	body	320	valid
296.0ms	463×	body	160	valid