Details

sample1.2s

Algorithm

intervals

Results

316.0ms	129×	body	1280	valid
300.0ms	73×	body	2560	valid
280.0ms	33×	body	5120	valid
215.0ms	87×	body	640	valid
31.0ms	28×	body	320	valid
25.0ms	67×	body	80	valid
10.0ms	14×	body	160	valid

simplify4.4s

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.9b

localize56.0ms

Local error

Found 4 expressions with local error:

6.9b	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
8.3b	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
12.8b	(* (/ k t) t)
12.8b	(* (/ k t) t)

rewrite327.0ms

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:

79.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
202.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
14.0ms	(* (/ k t) t)
13.0ms	(* (/ k t) t)

series444.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
391.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
12.0ms	(* (/ k t) t)
12.0ms	(* (/ k t) t)

simplify4.8s

Counts

361 → 361

Iterations

Iter	Nodes
2	10742
1	1954
0	616

prune1.5s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt 2) (tan k))
0.5b	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
2.0b	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
3.1b	(/ (* t (/ k 1)) (/ l (/ k 1)))

rewrite143.0ms

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))
15.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
68.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
15.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))

series952.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (sqrt 2) (tan k))
112.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
695.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
34.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))

simplify2.2s

Counts

1031 → 1031

Iterations

Iter	Nodes
1	4186
0	1291

prune6.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1))))
1.2b	(/ 1 (/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1)))))
2.1b	(* (/ 1 (/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1))))) (* (/ (sqrt 2) (* (/ k (cbrt l)) (cbrt k))) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))))
2.3b	(* (/ (sqrt 2) (* (/ k (cbrt l)) (cbrt k))) (/ (/ (* (sqrt 2) l) (tan k)) (sin k)))

rewrite477.0ms

Algorithm

rewrite-expression-head

Rules

3919×	`add-exp-log`
2159×	`div-exp`
1428×	`prod-exp`
1233×	`add-cbrt-cube`
1100×	`times-frac`
827×	`cbrt-undiv`
528×	`cbrt-unprod`
357×	`add-sqr-sqrt`
352×	`*-un-lft-identity` `add-cube-cbrt`
166×	`associate-l`
144×	`rec-exp` `1-exp`
78×	`sqrt-prod`
65×	`associate-/r*` `div-inv`
39×	`associate-/r/`
29×	`associate-r`
12×	`pow1`
6×	`frac-times` `associate-r/` `associate-/l`
5×	`associate-*l/`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`tan-quot`
2×	`clear-num` `frac-2neg` `*-commutative` `unswap-sqr`
1×	`pow-flip` `inv-pow`

Counts

4 → 1176

Calls

4 calls:

15.0ms	(/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1))))
21.0ms	(/ 1 (/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1)))))
256.0ms	(* (/ 1 (/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1))))) (* (/ (sqrt 2) (* (/ k (cbrt l)) (cbrt k))) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))))
105.0ms	(* (/ (sqrt 2) (* (/ k (cbrt l)) (cbrt k))) (/ (/ (* (sqrt 2) l) (tan k)) (sin k)))

series1.3s

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1))))
123.0ms	(/ 1 (/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1)))))
667.0ms	(* (/ 1 (/ t (/ (* (cbrt l) (cbrt l)) (/ (* (cbrt k) (cbrt k)) (sqrt 1))))) (* (/ (sqrt 2) (* (/ k (cbrt l)) (cbrt k))) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))))
392.0ms	(* (/ (sqrt 2) (* (/ k (cbrt l)) (cbrt k))) (/ (/ (* (sqrt 2) l) (tan k)) (sin k)))

simplify9.0s

Counts

1188 → 1188

Iterations

Iter	Nodes
1	4776
0	1528

prune7.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sqrt 2) l) (tan k))
0.5b	(* (sqrt 2) l)
2.0b	(/ (* (sqrt (sqrt 2)) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))) (/ t (/ (/ l k) k)))
4.6b	(/ t (/ (/ l k) k))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

1184×	`times-frac`
495×	`add-sqr-sqrt`
491×	`*-un-lft-identity` `add-cube-cbrt`
180×	`associate-/r*`
130×	`add-cbrt-cube` `add-exp-log`
78×	`cbrt-undiv` `div-exp`
45×	`div-inv`
22×	`prod-exp` `cbrt-unprod`
6×	`pow1` `associate-l`
5×	`associate-/r/` `associate-/l*`
4×	`sqrt-prod` `insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`unswap-sqr`
1×	`pow-prod-down` `tan-quot` `associate-r/` `-commutative` `associate-/l/`

Counts

4 → 561

Calls

4 calls:

12.0ms	(/ (* (sqrt 2) l) (tan k))
7.0ms	(* (sqrt 2) l)
45.0ms	(/ (* (sqrt (sqrt 2)) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))) (/ t (/ (/ l k) k)))
11.0ms	(/ t (/ (/ l k) k))

series846.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(/ (* (sqrt 2) l) (tan k))
58.0ms	(* (sqrt 2) l)
527.0ms	(/ (* (sqrt (sqrt 2)) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))) (/ t (/ (/ l k) k)))
42.0ms	(/ t (/ (/ l k) k))

simplify1.6s

Counts

573 → 573

Iterations

Iter	Nodes
1	3198
0	1002

prune5.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

regimes308.0ms

Accuracy

49.2% (2.7b remaining)

Error of 3.0b against oracle of 0.3b and baseline of 5.6b

bsearch688.0ms

Steps

Iters	Range		Point
6	5.365316158937965e+106	7.323076563744514e+107	1.6846040995988706e+107
8	-2.421296204998167e+170	-4.897051594830286e+167	-4.979647532007629e+167

simplify18.0ms

Iterations

Iter	Nodes
2	52
1	52
0	42

end0.0ms

sample39.9s

Algorithm

intervals

Results

11.6s	3932×	body	1280	valid
9.9s	2267×	body	2560	valid
7.7s	1003×	body	5120	valid
6.8s	2604×	body	640	valid
2.0s	977×	body	320	valid
977.0ms	1964×	body	80	valid
372.0ms	441×	body	160	valid