Details

sample1.6s

Algorithm

intervals

Results

738.0ms	73×	body	2560	valid
315.0ms	129×	body	1280	valid
275.0ms	33×	body	5120	valid
141.0ms	87×	body	640	valid
29.0ms	28×	body	320	valid
23.0ms	67×	body	80	valid
12.0ms	14×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2005
4	2005
3	1013
2	173
1	51
0	19

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin k) (tan k))
2.2b	(* (* (/ t l) (/ t l)) t)
2.3b	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
26.8b	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

662×	`add-cbrt-cube` `add-exp-log`
343×	`cbrt-undiv` `div-exp`
220×	`prod-exp` `cbrt-unprod`
57×	`times-frac`
25×	`associate-/l*`
21×	`associate-*l/`
20×	`add-sqr-sqrt`
18×	`associate-/r/`
17×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`associate-*r/`
8×	`div-inv`
6×	`frac-times` `associate-r`
4×	`associate-l` `pow-prod-down` `tan-quot` `insert-posit16` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 307

Calls

4 calls:

17.0ms	(* (sin k) (tan k))
57.0ms	(* (* (/ t l) (/ t l)) t)
82.0ms	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
90.0ms	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

series684.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (sin k) (tan k))
44.0ms	(* (* (/ t l) (/ t l)) t)
250.0ms	(/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k)))
327.0ms	(/ (/ (/ 2 (* (* (/ t l) (/ t l)) t)) (* (sin k) (tan k))) (* (/ k t) (/ k t)))

simplify1.1s

Counts

319 → 319

Iterations

Iter	Nodes
done	2001
2	2001
1	1335
0	468

prune4.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize77.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (/ 1 (* (/ t l) (/ t l))) (sin k))
4.6b	(* (/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ 2 t) (tan k)) (/ k t)))
12.7b	(/ (/ (/ 2 t) (tan k)) (/ k t))
17.4b	(/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t))

rewrite543.0ms

Algorithm

rewrite-expression-head

Rules

6616×	`times-frac`
2908×	`add-sqr-sqrt`
2549×	`*-un-lft-identity`
2535×	`add-cube-cbrt`
2263×	`add-exp-log`
1594×	`div-exp`
971×	`add-cbrt-cube`
663×	`cbrt-undiv`
577×	`associate-r`
449×	`prod-exp`
447×	`associate-l`
383×	`div-inv`
286×	`associate-/r/`
173×	`cbrt-unprod`
88×	`associate-/l*`
86×	`frac-times` `associate-l/` `associate-r/`
85×	`rec-exp` `1-exp`
63×	`unswap-sqr`
29×	`associate-/r*`
27×	`tan-quot`
6×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 2731

Calls

4 calls:

21.0ms	(/ (/ 1 (* (/ t l) (/ t l))) (sin k))
279.0ms	(* (/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ 2 t) (tan k)) (/ k t)))
31.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
36.0ms	(/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t))

series846.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (/ 1 (* (/ t l) (/ t l))) (sin k))
426.0ms	(* (/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t)) (/ (/ (/ 2 t) (tan k)) (/ k t)))
155.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))
183.0ms	(/ (/ (/ 1 (* (/ t l) (/ t l))) (sin k)) (/ k t))

simplify4.0s

Counts

2743 → 2743

Iterations

Iter	Nodes
done	3606
0	3606

prune47.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 5.9b

localize62.0ms

Local error

Found 4 expressions with local error:

2.3b	(/ (/ 1 (/ t l)) (sin k))
3.8b	(/ (/ (/ 1 (/ t l)) 1) k)
9.3b	(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))
12.7b	(/ (/ (/ 2 t) (tan k)) (/ k t))

rewrite291.0ms

Algorithm

rewrite-expression-head

Rules

11646×	`times-frac`
4790×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
492×	`div-inv`
360×	`associate-/l*`
211×	`add-exp-log`
176×	`div-exp`
80×	`add-cbrt-cube`
74×	`associate-/r/`
55×	`cbrt-undiv`
32×	`associate-/r*`
29×	`1-exp`
22×	`rec-exp`
14×	`tan-quot`
4×	`pow1` `clear-num` `frac-2neg` `insert-posit16` `add-log-exp` `associate-/l/`

Counts

4 → 3403

Calls

4 calls:

18.0ms	(/ (/ 1 (/ t l)) (sin k))
16.0ms	(/ (/ (/ 1 (/ t l)) 1) k)
27.0ms	(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))
37.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))

series357.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (/ 1 (/ t l)) (sin k))
35.0ms	(/ (/ (/ 1 (/ t l)) 1) k)
78.0ms	(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))
129.0ms	(/ (/ (/ 2 t) (tan k)) (/ k t))

simplify4.8s

Counts

3415 → 3415

Iterations

Iter	Nodes
done	5838
0	5838

prune1.1m

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.2b

localize100.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (/ (/ (/ 1 (/ t l)) 1) k) (* (/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t)) (* 2 (/ (cos k) (* k (sin k))))))
2.3b	(/ (/ 1 (/ t l)) (sin k))
3.8b	(/ (/ (/ 1 (/ t l)) 1) k)
9.3b	(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))

rewrite913.0ms

Algorithm

rewrite-expression-head

Rules

19614×	`add-exp-log`
13592×	`div-exp`
11143×	`times-frac`
6352×	`prod-exp`
4572×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2516×	`1-exp`
1729×	`add-cbrt-cube`
1578×	`rec-exp`
980×	`cbrt-undiv`
545×	`cbrt-unprod`
430×	`div-inv`
412×	`associate-l`
316×	`associate-/l*`
68×	`associate-/r/`
19×	`associate-/r*`
13×	`pow1`
9×	`associate-*r/`
6×	`pow-prod-down`
5×	`frac-times`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*l/` `associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 5494

Calls

4 calls:

329.0ms	(* (/ (/ (/ 1 (/ t l)) 1) k) (* (/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t)) (* 2 (/ (cos k) (* k (sin k))))))
25.0ms	(/ (/ 1 (/ t l)) (sin k))
16.0ms	(/ (/ (/ 1 (/ t l)) 1) k)
36.0ms	(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))

series636.0ms

Counts

4 → 12

Calls

4 calls:

340.0ms	(* (/ (/ (/ 1 (/ t l)) 1) k) (* (/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t)) (* 2 (/ (cos k) (* k (sin k))))))
128.0ms	(/ (/ 1 (/ t l)) (sin k))
40.0ms	(/ (/ (/ 1 (/ t l)) 1) k)
128.0ms	(/ (/ (/ 1 (/ t l)) (sin k)) (/ 1 t))

simplify9.0s

Counts

5506 → 5506

Iterations

Iter	Nodes
done	7504
0	7504

prune1.6m

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

regimes276.0ms

Accuracy

0% (2.2b remaining)

Error of 7.5b against oracle of 5.3b and baseline of 7.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	17

end0.0ms

sample26.8s

Algorithm

intervals

Results

7.7s	3932×	body	1280	valid
7.3s	2267×	body	2560	valid
6.0s	1003×	body	5120	valid
3.5s	2604×	body	640	valid
1.1s	977×	body	320	valid
522.0ms	1964×	body	80	valid
286.0ms	441×	body	160	valid