Details

sample370.0ms

Algorithm

intervals

Results

121.0ms	75×	body	1280	valid
68.0ms	201×	body	80	valid
64.0ms	57×	body	640	valid
21.0ms	27×	body	320	valid
5.0ms	11×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize43.0ms

Local error

Found 4 expressions with local error:

2.5b	(* (/ (pow t 3.0) (* l l)) (sin k))
4.1b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
14.7b	(/ (pow t 3.0) (* l l))
15.5b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

rewrite707.0ms

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:

36.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
84.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
16.0ms	(/ (pow t 3.0) (* l l))
564.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
460.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
288.0ms	(/ (pow t 3.0) (* l l))
797.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))

simplify1.6s

Counts

156 → 156

Iterations

Iter	Nodes
done	5000
1	820
0	254

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.5b

localize69.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
7.2b	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
9.7b	(* (/ (* (* t t) t) (* l l)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))
14.7b	(/ (* (* t t) t) (* l l))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

338×	`add-cbrt-cube` `add-exp-log`
165×	`prod-exp` `cbrt-unprod`
104×	`cbrt-undiv` `div-exp`
14×	`pow1`
13×	`associate-l`
11×	`add-sqr-sqrt` `frac-times` `associate-*r/`
9×	`-un-lft-identity` `times-frac` `associate-l/` `add-cube-cbrt`
8×	`associate-/r/`
6×	`pow-prod-down`
4×	`div-inv` `associate-/l*` `add-log-exp`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `unswap-sqr`
1×	`sin-mult`

Counts

4 → 214

Calls

4 calls:

58.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
69.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
116.0ms	(* (/ (* (* t t) t) (* l l)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))
41.0ms	(/ (* (* t t) t) (* l l))

series759.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
348.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
221.0ms	(* (/ (* (* t t) t) (* l l)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))
40.0ms	(/ (* (* t t) t) (* l l))

simplify1.4s

Counts

226 → 226

Iterations

Iter	Nodes
done	5001
1	1329
0	355

prune1.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 5.5b

localize100.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
1.4b	(/ (* (/ l t) (/ l t)) t)
7.2b	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
9.7b	(* (/ 1 (/ (* (/ l t) (/ l t)) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))

rewrite363.0ms

Algorithm

rewrite-expression-head

Rules

623×	`add-exp-log`
351×	`add-cbrt-cube`
268×	`prod-exp`
263×	`div-exp`
143×	`cbrt-undiv`
140×	`cbrt-unprod`
40×	`times-frac`
34×	`associate-l`
26×	`add-sqr-sqrt`
24×	`rec-exp` `*-un-lft-identity` `1-exp` `add-cube-cbrt`
14×	`pow1`
12×	`frac-times` `associate-*r/`
10×	`associate-*l/`
9×	`associate-/r/`
7×	`div-inv`
6×	`pow-prod-down`
4×	`associate-/r` `associate-/l` `add-log-exp`
3×	`associate-/l/`
2×	`clear-num` `frac-2neg` `associate-r` `*-commutative` `unswap-sqr`
1×	`sin-mult`

Counts

4 → 288

Calls

4 calls:

86.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
14.0ms	(/ (* (/ l t) (/ l t)) t)
53.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
178.0ms	(* (/ 1 (/ (* (/ l t) (/ l t)) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))

series819.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
59.0ms	(/ (* (/ l t) (/ l t)) t)
343.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
265.0ms	(* (/ 1 (/ (* (/ l t) (/ l t)) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))

simplify1.6s

Counts

300 → 300

Iterations

Iter	Nodes
done	5000
1	1913
0	488

prune1.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 4.9b

localize76.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
1.1b	(* (/ 1 (/ (/ l t) 1)) (* (/ 1 (/ (/ l t) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0)))
7.2b	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
11.3b	(* (/ 1 (/ (/ l t) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))

rewrite866.0ms

Algorithm

rewrite-expression-head

Rules

4724×	`add-exp-log`
2568×	`div-exp`
2080×	`prod-exp`
733×	`add-cbrt-cube`
661×	`times-frac`
655×	`1-exp`
409×	`rec-exp`
322×	`cbrt-undiv`
308×	`add-sqr-sqrt`
306×	`*-un-lft-identity` `add-cube-cbrt`
292×	`cbrt-unprod`
276×	`associate-l`
28×	`div-inv`
23×	`pow1`
16×	`frac-times` `associate-l/` `associate-r/`
12×	`pow-prod-down`
10×	`associate-/r/`
4×	`add-log-exp`
3×	`associate-r` `-commutative` `associate-/l`
2×	`unswap-sqr`
1×	`clear-num` `associate-/r*` `frac-2neg` `sin-mult`

Counts

4 → 1195

Calls

4 calls:

67.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
374.0ms	(* (/ 1 (/ (/ l t) 1)) (* (/ 1 (/ (/ l t) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0)))
72.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
152.0ms	(* (/ 1 (/ (/ l t) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))

series936.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k)))
271.0ms	(* (/ 1 (/ (/ l t) 1)) (* (/ 1 (/ (/ l t) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0)))
269.0ms	(/ t (* (/ (cos k) (* (sin k) (sin k))) (* (/ l k) (/ l k))))
207.0ms	(* (/ 1 (/ (/ l t) t)) (* (/ (* (sin k) (sin k)) (cos k)) 2.0))

simplify2.5s

Counts

1207 → 1207

Iterations

Iter	Nodes
done	5001
0	1692

prune5.6s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 4.9b

regimes1.3s

Accuracy

59.5% (3.7b remaining)

Error of 7.6b against oracle of 3.9b and baseline of 13.0b

bsearch517.0ms

Steps

Iters	Range		Point
11	2.42011835416667e-163	4.1021166797626e-139	3.02120870657335e-158
9	-8.100085967744099e-150	-1.9921920162605386e-158	-2.0589438665523545e-157

simplify12.0ms

Iterations

Iter	Nodes
done	65
1	65
0	48

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.8s	2016×	body	1280	valid
2.0s	1655×	body	640	valid
1.7s	5962×	body	80	valid
1.6s	883×	body	320	valid
211.0ms	452×	body	160	valid