Details

sample274.0ms

Algorithm

intervals

Results

94.0ms	65×	body	1280	valid
81.0ms	193×	body	80	valid
43.0ms	42×	body	640	valid
23.0ms	35×	body	320	valid
7.0ms	16×	body	160	valid

simplify3.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	4275
3	774
2	156
1	48
0	19

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize54.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (/ (pow t 3.0) (* l l)) (sin k))
2.5b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
13.9b	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
18.5b	(/ (pow t 3.0) (* l l))

rewrite750.0ms

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×	`expm1-log1p-u` `flip3-+` `flip-+` `log1p-expm1-u` `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 → 152

Calls

4 calls:

54.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
98.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
572.0ms	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
19.0ms	(/ (pow t 3.0) (* l l))

series2.1s

Counts

4 → 12

Calls

4 calls:

354.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
484.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.0s	(* (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k)) (+ (+ 1.0 (pow (/ k t) 2.0)) 1.0))
240.0ms	(/ (pow t 3.0) (* l l))

simplify2.6s

Counts

164 → 164

Iterations

Iter	Nodes
done	5016
2	3708
1	821
0	262

prune1.2s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.4b

localize85.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 2.0 (fma (* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l))) 2.0 (/ (/ (* (* (sin k) (sin k)) t) (* (/ l k) (/ l k))) (cos k))))
6.4b	(* (* (sin k) (sin k)) t)
7.4b	(/ (* (* (sin k) (sin k)) t) (* (/ l k) (/ l k)))
21.1b	(* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

182×	`add-cbrt-cube` `add-exp-log`
81×	`prod-exp` `cbrt-unprod`
59×	`cbrt-undiv` `div-exp`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
14×	`pow1`
13×	`times-frac`
8×	`associate-l`
6×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/`
4×	`expm1-log1p-u` `associate-/r` `associate-r` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`associate-/r/` `div-inv`
2×	`clear-num` `frac-2neg` `*-commutative` `sin-mult` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 168

Calls

4 calls:

7.0ms	(/ 2.0 (fma (* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l))) 2.0 (/ (/ (* (* (sin k) (sin k)) t) (* (/ l k) (/ l k))) (cos k))))
40.0ms	(* (* (sin k) (sin k)) t)
61.0ms	(/ (* (* (sin k) (sin k)) t) (* (/ l k) (/ l k)))
95.0ms	(* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

series1.1s

Counts

4 → 12

Calls

4 calls:

686.0ms	(/ 2.0 (fma (* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l))) 2.0 (/ (/ (* (* (sin k) (sin k)) t) (* (/ l k) (/ l k))) (cos k))))
79.0ms	(* (* (sin k) (sin k)) t)
134.0ms	(/ (* (* (sin k) (sin k)) t) (* (/ l k) (/ l k)))
227.0ms	(* (/ (* t (* t t)) (cos k)) (* (/ (sin k) l) (/ (sin k) l)))

simplify2.8s

Counts

180 → 180

Iterations

Iter	Nodes
done	5002
2	4595
1	1038
0	352

prune1.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 2.6b

localize122.0ms

Local error

Found 4 expressions with local error:

2.5b	(* t (/ (sin k) l))
2.5b	(* t (/ (sin k) l))
2.7b	(* (* (* t (/ (sin k) l)) (* t (/ (sin k) l))) t)
7.6b	(/ t (* (/ l k) (/ l k)))

rewrite255.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-cbrt-cube` `add-exp-log`
39×	`prod-exp` `cbrt-unprod`
34×	`add-sqr-sqrt`
29×	`associate-r`
26×	`pow1`
23×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
17×	`cbrt-undiv` `div-exp`
15×	`pow-prod-down`
8×	`associate-*r/`
7×	`associate-l`
5×	`associate-*l/` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r/` `-commutative` `div-inv` `associate-/l`
2×	`frac-times`
1×	`clear-num` `associate-/r*` `frac-2neg`

Counts

4 → 143

Calls

4 calls:

22.0ms	(* t (/ (sin k) l))
13.0ms	(* t (/ (sin k) l))
192.0ms	(* (* (* t (/ (sin k) l)) (* t (/ (sin k) l))) t)
18.0ms	(/ t (* (/ l k) (/ l k)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* t (/ (sin k) l))
80.0ms	(* t (/ (sin k) l))
146.0ms	(* (* (* t (/ (sin k) l)) (* t (/ (sin k) l))) t)
97.0ms	(/ t (* (/ l k) (/ l k)))

simplify2.4s

Counts

155 → 155

Iterations

Iter	Nodes
done	5002
2	3184
1	657
0	225

prune1.4s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 0.7b

localize89.0ms

Local error

Found 4 expressions with local error:

2.5b	(* t (/ (sin k) l))
2.5b	(* t (/ (sin k) l))
2.7b	(* (* (* t (/ (sin k) l)) (* t (/ (sin k) l))) t)
5.9b	(/ t (/ l k))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

95×	`times-frac`
74×	`add-sqr-sqrt`
66×	`add-cbrt-cube` `add-exp-log`
63×	`*-un-lft-identity` `add-cube-cbrt`
35×	`prod-exp` `cbrt-unprod`
29×	`associate-r`
26×	`pow1`
15×	`pow-prod-down`
13×	`associate-/r*`
11×	`cbrt-undiv` `div-exp`
7×	`associate-l` `associate-*r/` `div-inv`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
1×	`frac-times` `clear-num` `frac-2neg` `associate-/r/`

Counts

4 → 183

Calls

4 calls:

12.0ms	(* t (/ (sin k) l))
15.0ms	(* t (/ (sin k) l))
172.0ms	(* (* (* t (/ (sin k) l)) (* t (/ (sin k) l))) t)
8.0ms	(/ t (/ l k))

series316.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* t (/ (sin k) l))
80.0ms	(* t (/ (sin k) l))
119.0ms	(* (* (* t (/ (sin k) l)) (* t (/ (sin k) l))) t)
42.0ms	(/ t (/ l k))

simplify2.6s

Counts

195 → 195

Iterations

Iter	Nodes
done	5003
2	3381
1	826
0	300

prune1.8s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 0.7b

regimes822.0ms

Accuracy

0% (1.6b remaining)

Error of 2.2b against oracle of 0.5b and baseline of 2.2b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample10.8s

Algorithm

intervals

Results

4.3s	2063×	body	1280	valid
2.5s	1634×	body	640	valid
2.1s	5859×	body	80	valid
1.2s	887×	body	320	valid
203.0ms	413×	body	160	valid