Details

sample1.1s

Algorithm

intervals

Results

305.0ms	75×	body	2560	valid
290.0ms	136×	body	1280	valid
233.0ms	25×	body	5120	valid
162.0ms	75×	body	640	valid
56.0ms	31×	body	320	valid
26.0ms	75×	body	80	valid
10.0ms	14×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	1013
2	173
1	51
0	19

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.4b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ k t) (/ k t))
1.7b	(/ t (* (/ l t) (/ l t)))
3.8b	(/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k)))
26.9b	(/ (/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k))) (* (/ k t) (/ k t)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

672×	`add-cbrt-cube` `add-exp-log`
412×	`cbrt-undiv` `div-exp`
344×	`times-frac`
158×	`prod-exp` `cbrt-unprod`
116×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `add-cube-cbrt`
78×	`associate-/l*`
49×	`associate-/r/`
25×	`div-inv`
18×	`associate-*l/`
15×	`frac-times` `associate-*r/`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
4×	`insert-posit16` `add-log-exp` `unswap-sqr`
3×	`clear-num` `associate-/r*` `frac-2neg` `tan-quot`
2×	`associate-/l/`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 457

Calls

4 calls:

12.0ms	(* (/ k t) (/ k t))
10.0ms	(/ t (* (/ l t) (/ l t)))
24.0ms	(/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k)))
41.0ms	(/ (/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k))) (* (/ k t) (/ k t)))

series675.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (/ k t) (/ k t))
49.0ms	(/ t (* (/ l t) (/ l t)))
255.0ms	(/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k)))
343.0ms	(/ (/ (/ 2 (/ t (* (/ l t) (/ l t)))) (* (tan k) (sin k))) (* (/ k t) (/ k t)))

simplify1.9s

Counts

469 → 469

Iterations

Iter	Nodes
done	5001
1	2268
0	708

prune1.9s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.7b

localize32.0ms

Local error

Found 4 expressions with local error:

1.5b	(* (* (/ (/ k t) (/ l t)) (/ (/ k t) (/ l t))) (sin k))
5.8b	(/ (/ (/ 2 t) (tan k)) (* (* (/ (/ k t) (/ l t)) (/ (/ k t) (/ l t))) (sin k)))
15.0b	(/ (/ k t) (/ l t))
15.0b	(/ (/ k t) (/ l t))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

1018×	`times-frac`
821×	`add-cbrt-cube` `add-exp-log`
498×	`cbrt-undiv` `div-exp`
468×	`add-sqr-sqrt`
467×	`*-un-lft-identity` `add-cube-cbrt`
204×	`prod-exp` `cbrt-unprod`
70×	`associate-/l*`
67×	`div-inv`
27×	`associate-/r*`
9×	`pow1`
8×	`associate-*l/`
7×	`associate-/r/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `pow-prod-down` `associate-/l/`
2×	`frac-times` `tan-quot` `associate-*r/`
1×	`associate-l` `*-commutative` `unswap-sqr`

Counts

4 → 769

Calls

4 calls:

88.0ms	(* (* (/ (/ k t) (/ l t)) (/ (/ k t) (/ l t))) (sin k))
84.0ms	(/ (/ (/ 2 t) (tan k)) (* (* (/ (/ k t) (/ l t)) (/ (/ k t) (/ l t))) (sin k)))
16.0ms	(/ (/ k t) (/ l t))
9.0ms	(/ (/ k t) (/ l t))

series483.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* (* (/ (/ k t) (/ l t)) (/ (/ k t) (/ l t))) (sin k))
382.0ms	(/ (/ (/ 2 t) (tan k)) (* (* (/ (/ k t) (/ l t)) (/ (/ k t) (/ l t))) (sin k)))
20.0ms	(/ (/ k t) (/ l t))
9.0ms	(/ (/ k t) (/ l t))

simplify2.6s

Counts

781 → 781

Iterations

Iter	Nodes
done	5000
1	3244
0	1008

prune4.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (tan k))
0.3b	(/ (/ 1 (tan k)) (sin k))
3.7b	(* (/ (/ (/ 2 t) (/ k (/ l 1))) (/ k (/ l 1))) (/ (/ 1 (tan k)) (sin k)))
6.0b	(/ (/ 2 t) (/ k (/ l 1)))

rewrite6.7s

Algorithm

rewrite-expression-head

Rules

146732×	`times-frac`
55760×	`add-sqr-sqrt`
54813×	`*-un-lft-identity`
54708×	`add-cube-cbrt`
25393×	`associate-l`
6689×	`div-inv`
1360×	`add-exp-log`
1217×	`associate-/r/`
1097×	`div-exp`
491×	`add-cbrt-cube`
346×	`cbrt-undiv`
185×	`prod-exp`
148×	`unswap-sqr`
126×	`1-exp`
66×	`cbrt-unprod`
50×	`associate-/r*`
46×	`associate-r`
39×	`rec-exp`
30×	`associate-/l*`
8×	`tan-quot`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg`
2×	`associate-/l/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 26617

Calls

4 calls:

12.0ms	(/ 1 (tan k))
23.0ms	(/ (/ 1 (tan k)) (sin k))
2.6s	(* (/ (/ (/ 2 t) (/ k (/ l 1))) (/ k (/ l 1))) (/ (/ 1 (tan k)) (sin k)))
15.0ms	(/ (/ 2 t) (/ k (/ l 1)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1 (tan k))
69.0ms	(/ (/ 1 (tan k)) (sin k))
421.0ms	(* (/ (/ (/ 2 t) (/ k (/ l 1))) (/ k (/ l 1))) (/ (/ 1 (tan k)) (sin k)))
52.0ms	(/ (/ 2 t) (/ k (/ l 1)))

simplify41.5s

Counts

26629 → 26629

Iterations

Iter	Nodes
done	40706
0	40706

prune3.7m

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (tan k))
0.3b	(* (/ k (/ l 1)) (sin k))
1.3b	(* (/ (/ 2 t) (/ k (/ l 1))) (/ 1 (tan k)))
6.0b	(/ (/ 2 t) (/ k (/ l 1)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

3900×	`times-frac`
1759×	`add-sqr-sqrt`
1640×	`*-un-lft-identity`
1624×	`add-cube-cbrt`
621×	`associate-l`
209×	`add-exp-log`
205×	`div-inv`
135×	`div-exp`
101×	`add-cbrt-cube`
56×	`cbrt-undiv`
47×	`associate-/r*`
40×	`prod-exp`
32×	`associate-/r/`
31×	`unswap-sqr`
21×	`1-exp`
17×	`associate-r` `cbrt-unprod`
16×	`associate-/l*`
10×	`rec-exp`
9×	`pow1`
4×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `associate-l/` `tan-quot` `-commutative`
1×	`frac-times` `associate-*r/` `un-div-inv` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 1440

Calls

4 calls:

6.0ms	(/ 1 (tan k))
14.0ms	(* (/ k (/ l 1)) (sin k))
38.0ms	(* (/ (/ 2 t) (/ k (/ l 1))) (/ 1 (tan k)))
10.0ms	(/ (/ 2 t) (/ k (/ l 1)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (tan k))
51.0ms	(* (/ k (/ l 1)) (sin k))
168.0ms	(* (/ (/ 2 t) (/ k (/ l 1))) (/ 1 (tan k)))
42.0ms	(/ (/ 2 t) (/ k (/ l 1)))

simplify1.7s

Counts

1452 → 1452

Iterations

Iter	Nodes
done	5001
0	2018

prune7.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

regimes175.0ms

Accuracy

0% (1.4b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 1.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample25.8s

Algorithm

intervals

Results

7.4s	4153×	body	1280	valid
6.8s	2204×	body	2560	valid
5.7s	984×	body	5120	valid
3.3s	2448×	body	640	valid
1.1s	1028×	body	320	valid
567.0ms	2108×	body	80	valid
521.0ms	471×	body	160	valid