Details

sample250.0ms

Algorithm

intervals

Results

85.0ms	62×	body	1280	valid
69.0ms	183×	body	80	valid
46.0ms	57×	body	640	valid
16.0ms	27×	body	320	valid
6.0ms	16×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
3	873
2	158
1	48
0	19

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.8b

localize72.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
4.3b	(* (/ (pow t 3.0) (* l l)) (sin k))
15.4b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
15.6b	(/ (pow t 3.0) (* l l))

rewrite671.0ms

Algorithm

rewrite-expression-head

Rules

108×	`add-exp-log`
58×	`prod-exp`
52×	`add-cbrt-cube`
26×	`cbrt-unprod`
24×	`div-exp`
21×	`add-sqr-sqrt`
20×	`pow1`
19×	`*-un-lft-identity`
17×	`times-frac`
16×	`associate-*l/`
14×	`add-cube-cbrt`
13×	`associate-l`
11×	`associate-r`
10×	`frac-times` `unpow-prod-down` `pow-prod-down`
8×	`pow-to-exp` `cbrt-undiv` `pow-exp` `tan-quot`
7×	`associate-/l*`
6×	`associate-*r/`
4×	`flip3-+` `flip-+` `add-log-exp` `unswap-sqr` `sqr-pow`
3×	`*-commutative` `distribute-lft-out`
2×	`div-inv`
1×	`distribute-rgt-in` `clear-num` `associate-/r*` `frac-2neg` `distribute-lft-in`

Counts

4 → 144

Calls

4 calls:

92.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
38.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
519.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
17.0ms	(/ (pow t 3.0) (* l l))

series2.1s

Counts

4 → 12

Calls

4 calls:

594.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
356.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
903.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
216.0ms	(/ (pow t 3.0) (* l l))

simplify1.5s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
1	822
0	254

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 15.6b

localize86.0ms

Local error

Found 4 expressions with local error:

3.4b	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
4.3b	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
8.4b	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
15.4b	(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

346×	`add-exp-log`
203×	`prod-exp`
97×	`div-exp`
82×	`add-cbrt-cube`
55×	`associate-*l/`
46×	`cbrt-unprod`
41×	`pow-exp`
35×	`frac-times`
32×	`pow1`
28×	`pow-to-exp`
22×	`*-un-lft-identity`
19×	`pow-prod-down`
17×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`tan-quot`
15×	`times-frac` `associate-*r/`
13×	`cbrt-undiv`
11×	`associate-r`
8×	`flip3-+` `flip-+`
5×	`associate-/l*`
4×	`unpow-prod-down` `add-log-exp` `sqr-pow`
3×	`associate-/r` `associate-l` `-commutative` `distribute-lft-out`
1×	`distribute-rgt-in` `clear-num` `frac-2neg` `distribute-lft-in` `div-inv`

Counts

4 → 204

Calls

4 calls:

251.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
61.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
14.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s	(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series2.4s

Counts

4 → 12

Calls

4 calls:

617.0ms	(* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k))
352.0ms	(* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k))
331.0ms	(/ (pow (* (cbrt t) (cbrt t)) 3.0) l)
1.1s	(* (* (* (* (/ (pow (* (cbrt t) (cbrt t)) 3.0) l) (/ (pow (cbrt t) 3.0) l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.9s

Counts

216 → 216

Iterations

Iter	Nodes
done	5000
1	1195
0	370

prune1.6s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 6.6b

localize106.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 2.0 (+ (/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))) (* 2.0 (* (* (/ (sin k) l) (/ (sin k) l)) (/ (* (* t t) t) (cos k))))))
1.9b	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
7.4b	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
20.0b	(* (* (/ (sin k) l) (/ (sin k) l)) (/ (* (* t t) t) (cos k)))

rewrite776.0ms

Algorithm

rewrite-expression-head

Rules

263×	`add-cbrt-cube` `add-exp-log`
115×	`prod-exp` `cbrt-unprod`
92×	`cbrt-undiv` `div-exp`
23×	`associate-*r/`
21×	`add-sqr-sqrt`
20×	`frac-times`
19×	`times-frac`
18×	`*-un-lft-identity` `add-cube-cbrt`
17×	`associate-/r/`
16×	`associate-*l/`
14×	`pow1`
9×	`associate-l`
8×	`associate-r`
7×	`frac-add`
6×	`pow-prod-down` `associate-/l*`
4×	`associate-/r*` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`flip3-+` `flip-+` `sin-mult`

Counts

4 → 216

Calls

4 calls:

133.0ms	(/ 2.0 (+ (/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))) (* 2.0 (* (* (/ (sin k) l) (/ (sin k) l)) (/ (* (* t t) t) (cos k))))))
66.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
52.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
501.0ms	(* (* (/ (sin k) l) (/ (sin k) l)) (/ (* (* t t) t) (cos k)))

series1.6s

Counts

4 → 12

Calls

4 calls:

705.0ms	(/ 2.0 (+ (/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))) (* 2.0 (* (* (/ (sin k) l) (/ (sin k) l)) (/ (* (* t t) t) (cos k))))))
192.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
355.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
342.0ms	(* (* (/ (sin k) l) (/ (sin k) l)) (/ (* (* t t) t) (cos k)))

simplify1.5s

Counts

228 → 228

Iterations

Iter	Nodes
done	5000
1	1482
0	430

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 2.5b

localize74.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (* (* (/ (sin k) l) t) (* (/ (sin k) l) t)) t)
3.7b	(* (/ (sin k) l) t)
3.7b	(* (/ (sin k) l) t)
7.4b	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))

rewrite313.0ms

Algorithm

rewrite-expression-head

Rules

147×	`add-cbrt-cube` `add-exp-log`
67×	`prod-exp` `cbrt-unprod`
46×	`cbrt-undiv` `div-exp`
34×	`add-sqr-sqrt`
27×	`associate-l`
26×	`pow1`
23×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
15×	`pow-prod-down`
13×	`associate-*l/`
9×	`associate-r`
7×	`associate-/r/`
6×	`frac-times` `associate-*r/`
5×	`unswap-sqr`
4×	`add-log-exp`
3×	`-commutative` `div-inv` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg`

Counts

4 → 161

Calls

4 calls:

197.0ms	(* (* (* (/ (sin k) l) t) (* (/ (sin k) l) t)) t)
25.0ms	(* (/ (sin k) l) t)
13.0ms	(* (/ (sin k) l) t)
69.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))

series764.0ms

Counts

4 → 12

Calls

4 calls:

261.0ms	(* (* (* (/ (sin k) l) t) (* (/ (sin k) l) t)) t)
96.0ms	(* (/ (sin k) l) t)
82.0ms	(* (/ (sin k) l) t)
324.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))

simplify1.4s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
1	1085
0	313

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 1.7b

regimes1.0s

Accuracy

21.2% (4.1b remaining)

Error of 5.5b against oracle of 1.4b and baseline of 6.6b

bsearch6.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	52
1	52
0	37

end0.0ms

sample10.4s

Algorithm

intervals

Results

3.7s	2026×	body	1280	valid
2.4s	5830×	body	80	valid
2.1s	1748×	body	640	valid
1.6s	834×	body	320	valid
220.0ms	407×	body	160	valid