Details

sample1.2s

Algorithm

intervals

Results

404.0ms	68×	body	2560	valid
322.0ms	127×	body	1280	valid
157.0ms	82×	body	640	valid
151.0ms	20×	body	5120	valid
77.0ms	54×	body	80	valid
43.0ms	32×	body	320	valid
6.0ms	7×	body	160	valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
4	7081
3	997
2	172
1	49
0	19

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.3b

localize58.0ms

Local error

Found 4 expressions with local error:

7.7b	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
12.3b	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
13.8b	(* (/ k t) t)
13.8b	(* (/ k t) t)

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

589×	`add-cbrt-cube` `add-exp-log`
252×	`cbrt-undiv` `div-exp`
250×	`prod-exp` `cbrt-unprod`
199×	`times-frac`
102×	`add-sqr-sqrt`
92×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-/l*`
26×	`associate-l`
12×	`div-inv`
8×	`pow1` `associate-*l/`
6×	`associate-r`
5×	`associate-/r/`
4×	`associate-/r` `associate-r/` `insert-posit16` `add-log-exp` `unswap-sqr` `associate-/l/`
2×	`frac-times` `clear-num` `frac-2neg` `pow-prod-down` `tan-quot` `*-commutative`

Counts

4 → 349

Calls

4 calls:

52.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
194.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
18.0ms	(* (/ k t) t)
9.0ms	(* (/ k t) t)

series804.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
760.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
7.0ms	(* (/ k t) t)
7.0ms	(* (/ k t) t)

simplify5.6s

Counts

361 → 361

Iterations

Iter	Nodes
2	10742
1	1954
0	616

prune5.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.5b

localize63.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt 2) (tan k))
0.6b	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
2.8b	(/ (* t (/ k 1)) (/ l (/ k 1)))
3.7b	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

2212×	`times-frac`
801×	`add-exp-log`
756×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
483×	`div-exp`
472×	`add-cbrt-cube`
309×	`sqrt-prod`
299×	`associate-l`
252×	`cbrt-undiv`
246×	`prod-exp`
141×	`cbrt-unprod`
96×	`associate-/r*`
77×	`div-inv`
56×	`1-exp`
32×	`associate-/r/`
13×	`associate-/l*`
9×	`pow1`
6×	`associate-*r/`
5×	`frac-times`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/`
1×	`associate-r` `tan-quot` `*-commutative` `associate-/l/`

Counts

4 → 1019

Calls

4 calls:

6.0ms	(/ (sqrt 2) (tan k))
24.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
20.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))
91.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))

series958.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (sqrt 2) (tan k))
148.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
51.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))
668.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))

simplify2.4s

Counts

1031 → 1031

Iterations

Iter	Nodes
1	4199
0	1291

prune17.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt 2) (tan k))
0.5b	(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
2.7b	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k)))))
2.8b	(/ t (/ l k))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

588×	`add-exp-log`
482×	`add-cbrt-cube`
254×	`prod-exp` `cbrt-unprod`
240×	`cbrt-undiv` `div-exp`
230×	`times-frac`
116×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
80×	`associate-l`
22×	`frac-times` `associate-*r/`
21×	`sqrt-prod`
18×	`cbrt-prod` `pow1`
16×	`associate-/r*`
12×	`div-inv`
10×	`associate-*l/`
9×	`pow-prod-down` `associate-/l*`
4×	`associate-/r/` `insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`
1×	`tan-quot`

Counts

4 → 413

Calls

4 calls:

7.0ms	(/ (sqrt 2) (tan k))
46.0ms	(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
138.0ms	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k)))))
6.0ms	(/ t (/ l k))

series1.2s

Counts

4 → 12

Calls

4 calls:

66.0ms	(/ (sqrt 2) (tan k))
575.0ms	(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
548.0ms	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt 2) (tan k)) (/ l (sin k)))))
26.0ms	(/ t (/ l k))

simplify6.2s

Counts

425 → 425

Iterations

Iter	Nodes
2	10270
1	1996
0	666

prune7.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize89.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
0.5b	(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt (sqrt 2)) (/ (tan k) (sqrt (sqrt 2)))) (/ l (sin k))))
2.7b	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt (sqrt 2)) (/ (tan k) (sqrt (sqrt 2)))) (/ l (sin k)))))
2.8b	(/ t (/ l k))

rewrite390.0ms

Algorithm

rewrite-expression-head

Rules

887×	`add-exp-log`
735×	`add-cbrt-cube`
395×	`cbrt-undiv` `div-exp`
388×	`times-frac`
361×	`prod-exp` `cbrt-unprod`
171×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
80×	`associate-l`
57×	`associate-/r*`
22×	`frac-times` `associate-*r/`
20×	`div-inv`
18×	`cbrt-prod` `pow1`
10×	`associate-*l/`
9×	`pow-prod-down` `sqrt-prod`
6×	`associate-/r/`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative`

Counts

4 → 549

Calls

4 calls:

13.0ms	(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
83.0ms	(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt (sqrt 2)) (/ (tan k) (sqrt (sqrt 2)))) (/ l (sin k))))
249.0ms	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt (sqrt 2)) (/ (tan k) (sqrt (sqrt 2)))) (/ l (sin k)))))
11.0ms	(/ t (/ l k))

series1.7s

Counts

4 → 12

Calls

4 calls:

420.0ms	(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
603.0ms	(* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt (sqrt 2)) (/ (tan k) (sqrt (sqrt 2)))) (/ l (sin k))))
679.0ms	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (cbrt (sqrt 2)) k) (* (/ (sqrt (sqrt 2)) (/ (tan k) (sqrt (sqrt 2)))) (/ l (sin k)))))
36.0ms	(/ t (/ l k))

simplify1.8s

Counts

561 → 561

Iterations

Iter	Nodes
1	2679
0	783

prune11.4s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes351.0ms

Accuracy

0% (1.2b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 1.2b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	24
1	24
0	20

end0.0ms

sample42.9s

Algorithm

intervals

Results

13.8s	4130×	body	1280	valid
10.7s	2169×	body	2560	valid
8.5s	1001×	body	5120	valid
6.2s	2481×	body	640	valid
1.3s	2043×	body	80	valid
1.3s	958×	body	320	valid
450.0ms	418×	body	160	valid