Details

sample1.1s

Algorithm

intervals

Results

316.0ms	65×	body	2560	valid
246.0ms	103×	body	1280	valid
233.0ms	28×	body	5120	valid
142.0ms	76×	body	640	valid
45.0ms	43×	body	320	valid
28.0ms	66×	body	80	valid
15.0ms	19×	body	160	valid

simplify4.9s

Counts

1 → 1

Iterations

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 15.5b

localize63.0ms

Local error

Found 4 expressions with local error:

6.5b	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
11.5b	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
13.0b	(* (/ k t) t)
13.0b	(* (/ k t) t)

rewrite326.0ms

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:

51.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
232.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
10.0ms	(* (/ k t) t)
10.0ms	(* (/ k t) t)

series436.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
386.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
12.0ms	(* (/ k t) t)
12.0ms	(* (/ k t) t)

simplify5.7s

Counts

361 → 361

Iterations

Iter	Nodes
2	10742
1	1954
0	616

prune5.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.6b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt 2) (tan k))
0.9b	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
2.7b	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
3.3b	(/ (* t (/ k 1)) (/ l (/ k 1)))

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:

12.0ms	(/ (sqrt 2) (tan k))
26.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
65.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
20.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))

series917.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(/ (sqrt 2) (tan k))
168.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
636.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
33.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))

simplify2.3s

Counts

1031 → 1031

Iterations

Iter	Nodes
1	4186
0	1291

prune17.0s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (sqrt 2) l)
0.5b	(/ (sqrt (sqrt 2)) (/ t (/ l k)))
2.8b	(/ t (/ l k))
3.3b	(* (/ (sqrt (sqrt 2)) (/ t (/ l k))) (/ (* (sqrt (sqrt 2)) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))) k))

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

2142×	`times-frac`
1026×	`add-sqr-sqrt`
984×	`*-un-lft-identity` `add-cube-cbrt`
814×	`sqrt-prod`
407×	`associate-l`
164×	`add-cbrt-cube` `add-exp-log`
85×	`cbrt-undiv` `div-exp`
84×	`div-inv`
57×	`associate-/r*`
45×	`prod-exp` `cbrt-unprod`
22×	`associate-/r/`
12×	`associate-/l*` `unswap-sqr`
10×	`associate-r`
8×	`pow1`
4×	`insert-posit16` `add-log-exp`
2×	`clear-num` `frac-2neg` `pow-prod-down` `*-commutative`
1×	`frac-times` `associate-l/` `associate-r/`

Counts

4 → 1040

Calls

4 calls:

14.0ms	(* (sqrt 2) l)
23.0ms	(/ (sqrt (sqrt 2)) (/ t (/ l k)))
11.0ms	(/ t (/ l k))
97.0ms	(* (/ (sqrt (sqrt 2)) (/ t (/ l k))) (/ (* (sqrt (sqrt 2)) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))) k))

series835.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (sqrt 2) l)
139.0ms	(/ (sqrt (sqrt 2)) (/ t (/ l k)))
43.0ms	(/ t (/ l k))
575.0ms	(* (/ (sqrt (sqrt 2)) (/ t (/ l k))) (/ (* (sqrt (sqrt 2)) (/ (/ (* (sqrt 2) l) (tan k)) (sin k))) k))

simplify3.2s

Counts

1052 → 1052

Iterations

Iter	Nodes
1	3676
0	1116

prune19.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (/ t (/ l k)))
1.0b	(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))
2.8b	(/ t (/ l k))
3.3b	(* (/ (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (/ t (/ l k))) (/ (/ (/ (* (sqrt 2) l) (tan k)) (sin k)) k))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

574×	`times-frac`
313×	`add-sqr-sqrt`
247×	`add-cbrt-cube` `add-exp-log`
238×	`*-un-lft-identity` `add-cube-cbrt`
138×	`cbrt-undiv` `div-exp`
97×	`associate-r`
66×	`sqrt-prod`
61×	`prod-exp` `cbrt-unprod`
58×	`associate-l`
57×	`associate-/r*`
32×	`sqrt-pow1` `div-inv`
29×	`pow1`
21×	`unswap-sqr`
16×	`pow1/2`
15×	`swap-sqr` `associate-/r/`
9×	`tan-quot` `pow-prod-up`
6×	`pow-prod-down`
5×	`pow-sqr`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`pow2` `frac-times` `rem-square-sqrt` `pow-plus` `sqrt-unprod` `associate-l/` `associate-r/`

Counts

4 → 492

Calls

4 calls:

19.0ms	(/ (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (/ t (/ l k)))
27.0ms	(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))
11.0ms	(/ t (/ l k))
103.0ms	(* (/ (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (/ t (/ l k))) (/ (/ (/ (* (sqrt 2) l) (tan k)) (sin k)) k))

series827.0ms

Counts

4 → 10

Calls

4 calls:

149.0ms	(/ (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (/ t (/ l k)))
0.0ms	(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))
30.0ms	(/ t (/ l k))
648.0ms	(* (/ (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (/ t (/ l k))) (/ (/ (/ (* (sqrt 2) l) (tan k)) (sin k)) k))

simplify1.9s

Counts

502 → 502

Iterations

Iter	Nodes
1	2552
0	793

prune7.8s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes366.0ms

Accuracy

78.2% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 2.8b

bsearch1.4s

Steps

Iters	Range		Point
10	5.8047538445884514e-133	8.422535045918206e-117	8.256232424735127e-117
7	-13444383639046.232	-265991755648.13324	-1928263201893.6716

simplify14.0ms

Iterations

Iter	Nodes
2	39
1	39
0	32

end0.0ms

sample41.1s

Algorithm

intervals

Results

11.0s	4149×	body	1280	valid
10.9s	2174×	body	2560	valid
10.0s	980×	body	5120	valid
5.5s	2510×	body	640	valid
1.4s	1061×	body	320	valid
1.3s	2122×	body	80	valid
368.0ms	447×	body	160	valid