Details

sample443.0ms

Algorithm

intervals

Results

183.0ms	72×	body	1280	valid
114.0ms	71×	body	640	valid
82.0ms	187×	body	80	valid
29.0ms	27×	body	320	valid
7.0ms	7×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
4	2000
3	1118
2	185
1	54
0	19

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.9b

localize34.0ms

Local error

Found 4 expressions with local error:

2.0b	(* (* (/ t l) (/ t l)) t)
2.0b	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
3.7b	(* (sin k) (* (* (/ t l) (/ t l)) t))
13.4b	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

rewrite406.0ms

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:

33.0ms	(* (* (/ t l) (/ t l)) t)
109.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
92.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
161.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

series1.3s

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* (/ t l) (/ t l)) t)
333.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t)))
131.0ms	(* (sin k) (* (* (/ t l) (/ t l)) t))
818.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (* (/ t l) (/ t l)) t))) (+ (* (/ k t) (/ k t)) 2))

simplify1.4s

Counts

275 → 275

Iterations

Iter	Nodes
done	2001
2	2001
1	1235
0	448

prune1.9s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ k t) (/ k t))
2.0b	(/ (/ 2 (tan k)) (* (sin k) (* (/ t l) (* (/ t l) t))))
3.7b	(* (sin k) (* (/ t l) (* (/ t l) t)))
13.4b	(/ (/ (/ 2 (tan k)) (* (sin k) (* (/ t l) (* (/ t l) t)))) (+ (* (/ k t) (/ k t)) 2))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

231×	`add-cbrt-cube` `add-exp-log`
227×	`times-frac`
113×	`add-sqr-sqrt`
101×	`*-un-lft-identity` `add-cube-cbrt`
94×	`cbrt-undiv` `div-exp`
89×	`prod-exp` `cbrt-unprod`
35×	`associate-/l*`
25×	`associate-*r/`
23×	`associate-/r/`
20×	`pow1`
19×	`associate-*l/`
16×	`associate-l` `div-inv`
14×	`associate-r`
13×	`swap-sqr`
7×	`frac-times` `pow-prod-down`
6×	`tan-quot`
4×	`associate-/r*` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative` `associate-/l/`
1×	`pow2` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 312

Calls

4 calls:

16.0ms	(* (/ k t) (/ k t))
102.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (/ t l) (* (/ t l) t))))
107.0ms	(* (sin k) (* (/ t l) (* (/ t l) t)))
156.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (/ t l) (* (/ t l) t)))) (+ (* (/ k t) (/ k t)) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ k t) (/ k t))
331.0ms	(/ (/ 2 (tan k)) (* (sin k) (* (/ t l) (* (/ t l) t))))
177.0ms	(* (sin k) (* (/ t l) (* (/ t l) t)))
884.0ms	(/ (/ (/ 2 (tan k)) (* (sin k) (* (/ t l) (* (/ t l) t)))) (+ (* (/ k t) (/ k t)) 2))

simplify1.7s

Counts

324 → 324

Iterations

Iter	Nodes
done	2005
2	2005
1	1599
0	541

prune2.0s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 12.2b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ k t) (/ k t))
2.0b	(/ (/ 2 (tan k)) (* (* (sin k) (/ t l)) (* (/ t l) t)))
3.8b	(* (sin k) (/ t l))
13.4b	(/ (/ (/ 2 (tan k)) (* (* (sin k) (/ t l)) (* (/ t l) t))) (+ (* (/ k t) (/ k t)) 2))

rewrite594.0ms

Algorithm

rewrite-expression-head

Rules

251×	`add-cbrt-cube` `add-exp-log`
237×	`times-frac`
125×	`add-sqr-sqrt`
110×	`cbrt-undiv` `div-exp`
108×	`*-un-lft-identity` `add-cube-cbrt`
90×	`prod-exp` `cbrt-unprod`
35×	`associate-/l*`
26×	`associate-r`
23×	`associate-/r/`
17×	`associate-*r/` `div-inv`
16×	`associate-l` `associate-*l/`
13×	`pow1` `swap-sqr`
6×	`frac-times` `tan-quot` `unswap-sqr`
4×	`associate-/r*` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative` `associate-/l/`
1×	`pow2` `flip3-+` `pow-plus` `pow-sqr` `pow-prod-up` `flip-+`

Counts

4 → 328

Calls

4 calls:

12.0ms	(* (/ k t) (/ k t))
52.0ms	(/ (/ 2 (tan k)) (* (* (sin k) (/ t l)) (* (/ t l) t)))
22.0ms	(* (sin k) (/ t l))
500.0ms	(/ (/ (/ 2 (tan k)) (* (* (sin k) (/ t l)) (* (/ t l) t))) (+ (* (/ k t) (/ k t)) 2))

series1.4s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (/ k t) (/ k t))
375.0ms	(/ (/ 2 (tan k)) (* (* (sin k) (/ t l)) (* (/ t l) t)))
74.0ms	(* (sin k) (/ t l))
908.0ms	(/ (/ (/ 2 (tan k)) (* (* (sin k) (/ t l)) (* (/ t l) t))) (+ (* (/ k t) (/ k t)) 2))

simplify1.4s

Counts

340 → 340

Iterations

Iter	Nodes
done	2006
2	2006
1	1724
0	572

prune2.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.4b

localize54.0ms

Local error

Found 4 expressions with local error:

3.2b	(/ (/ (sqrt 2) (tan k)) (* (/ t l) t))
3.8b	(* (sin k) (/ t l))
5.8b	(/ (/ (/ (sqrt 2) 1) (* (sin k) (/ t l))) (/ (+ (* (/ k t) (/ k t)) 2) (/ (/ (sqrt 2) (tan k)) (* (/ t l) t))))
10.8b	(/ (+ (* (/ k t) (/ k t)) 2) (/ (/ (sqrt 2) (tan k)) (* (/ t l) t)))

rewrite373.0ms

Algorithm

rewrite-expression-head

Rules

12116×	`times-frac`
3376×	`add-sqr-sqrt`
3371×	`*-un-lft-identity` `add-cube-cbrt`
1620×	`sqrt-prod`
607×	`add-exp-log`
445×	`add-cbrt-cube`
434×	`div-exp`
390×	`div-inv`
300×	`cbrt-undiv`
299×	`associate-/r/`
118×	`associate-/r*`
98×	`prod-exp`
91×	`associate-*r/`
90×	`tan-quot`
89×	`associate-*l/`
70×	`cbrt-unprod`
53×	`associate-/l*`
24×	`1-exp`
13×	`associate-r`
6×	`pow1`
4×	`insert-posit16` `add-log-exp` `associate-/l/`
3×	`clear-num` `frac-2neg` `associate-l`
2×	`unswap-sqr`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 2916

Calls

4 calls:

33.0ms	(/ (/ (sqrt 2) (tan k)) (* (/ t l) t))
24.0ms	(* (sin k) (/ t l))
63.0ms	(/ (/ (/ (sqrt 2) 1) (* (sin k) (/ t l))) (/ (+ (* (/ k t) (/ k t)) 2) (/ (/ (sqrt 2) (tan k)) (* (/ t l) t))))
64.0ms	(/ (+ (* (/ k t) (/ k t)) 2) (/ (/ (sqrt 2) (tan k)) (* (/ t l) t)))

series2.2s

Counts

4 → 12

Calls

4 calls:

307.0ms	(/ (/ (sqrt 2) (tan k)) (* (/ t l) t))
77.0ms	(* (sin k) (/ t l))
1.3s	(/ (/ (/ (sqrt 2) 1) (* (sin k) (/ t l))) (/ (+ (* (/ k t) (/ k t)) 2) (/ (/ (sqrt 2) (tan k)) (* (/ t l) t))))
427.0ms	(/ (+ (* (/ k t) (/ k t)) 2) (/ (/ (sqrt 2) (tan k)) (* (/ t l) t)))

simplify5.0s

Counts

2928 → 2928

Iterations

Iter	Nodes
done	4052
0	4052

prune22.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 6.9b

regimes401.0ms

Accuracy

67.3% (1.6b remaining)

Error of 9.0b against oracle of 7.3b and baseline of 12.3b

bsearch552.0ms

Steps

Iters	Range		Point
7	6908.433222809883	657359.5389414565	368905.46702557366
7	-5.416718010051998e+66	-5.981261346914101e+64	-1.0373876915132293e+65

simplify25.0ms

Iterations

Iter	Nodes
done	66
1	66
0	53

end0.0ms

sample16.0s

Algorithm

intervals

Results

6.6s	2126×	body	1280	valid
3.8s	1770×	body	640	valid
2.7s	5859×	body	80	valid
1.7s	882×	body	320	valid
818.0ms	394×	body	160	valid