Details

sample1.2s

Algorithm

intervals

Results

313.0ms	117×	body	1280	valid
297.0ms	31×	body	5120	valid
283.0ms	64×	body	2560	valid
176.0ms	95×	body	640	valid
38.0ms	34×	body	320	valid
22.0ms	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

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.4b

localize43.0ms

Local error

Found 4 expressions with local error:

8.9b	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
10.4b	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
12.7b	(* (/ k t) t)
12.7b	(* (/ k t) t)

rewrite379.0ms

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:

83.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
238.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
16.0ms	(* (/ k t) t)
20.0ms	(* (/ k t) t)

series427.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (* (* (/ k t) t) (* (/ k t) t)) l)
367.0ms	(/ (/ 2 (/ t l)) (* (/ (* (* (/ k t) t) (* (/ k t) t)) l) (* (sin k) (tan k))))
18.0ms	(* (/ k t) t)
12.0ms	(* (/ k t) t)

simplify5.6s

Counts

361 → 361

Iterations

Iter	Nodes
2	10742
1	1954
0	616

prune5.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
0.5b	(/ (sqrt 2) (tan k))
1.9b	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
2.2b	(/ (* t (/ k 1)) (/ l (/ k 1)))

rewrite216.0ms

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:

31.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
15.0ms	(/ (sqrt 2) (tan k))
87.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
30.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))

series954.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1))))
108.0ms	(/ (sqrt 2) (tan k))
671.0ms	(* (/ (sqrt 2) (/ (* t (/ k 1)) (/ l (/ k 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
42.0ms	(/ (* t (/ k 1)) (/ l (/ k 1)))

simplify2.2s

Counts

1031 → 1031

Iterations

Iter	Nodes
1	4179
0	1291

prune17.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize102.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt l)
0.6b	(* (/ t (/ (* (cbrt l) (cbrt l)) k)) (/ k (/ (cbrt l) 1)))
1.9b	(* (/ (sqrt 2) (* (/ t (/ (* (cbrt l) (cbrt l)) k)) (/ k (/ (cbrt l) 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
3.4b	(/ t (/ (* (cbrt l) (cbrt l)) k))

rewrite293.0ms

Algorithm

rewrite-expression-head

Rules

774×	`add-exp-log`
532×	`add-cbrt-cube`
402×	`div-exp`
288×	`cbrt-undiv`
283×	`prod-exp`
234×	`times-frac`
217×	`cbrt-unprod`
169×	`add-sqr-sqrt`
106×	`*-un-lft-identity`
100×	`add-cube-cbrt`
72×	`associate-r`
39×	`associate-l`
36×	`cbrt-prod`
24×	`1-exp`
18×	`unswap-sqr`
14×	`div-inv`
11×	`pow1`
7×	`frac-times` `associate-/r` `associate-r/`
6×	`associate-/r/`
5×	`associate-*l/`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`sqrt-prod` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `pow1/3`

Counts

4 → 409

Calls

4 calls:

1.0ms	(cbrt l)
57.0ms	(* (/ t (/ (* (cbrt l) (cbrt l)) k)) (/ k (/ (cbrt l) 1)))
196.0ms	(* (/ (sqrt 2) (* (/ t (/ (* (cbrt l) (cbrt l)) k)) (/ k (/ (cbrt l) 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
16.0ms	(/ t (/ (* (cbrt l) (cbrt l)) k))

series1.1s

Counts

4 → 12

Calls

4 calls:

250.0ms	(cbrt l)
79.0ms	(* (/ t (/ (* (cbrt l) (cbrt l)) k)) (/ k (/ (cbrt l) 1)))
649.0ms	(* (/ (sqrt 2) (* (/ t (/ (* (cbrt l) (cbrt l)) k)) (/ k (/ (cbrt l) 1)))) (* (/ (sqrt 2) (tan k)) (/ l (sin k))))
171.0ms	(/ t (/ (* (cbrt l) (cbrt l)) k))

simplify1.5s

Counts

421 → 421

Iterations

Iter	Nodes
1	2387
0	698

prune7.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0b

localize56.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (sqrt 2) (tan k))
1.0b	(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
2.9b	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (* (/ (sqrt 2) (tan k)) l) (sin k)) (/ (cbrt (sqrt 2)) k)))
3.7b	(/ t (/ l k))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

461×	`add-exp-log`
379×	`times-frac`
373×	`add-cbrt-cube`
208×	`cbrt-undiv` `div-exp`
177×	`prod-exp` `cbrt-unprod`
167×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
60×	`associate-/r*`
49×	`associate-l`
20×	`div-inv`
12×	`sqrt-prod`
10×	`associate-/l*`
9×	`pow1`
7×	`associate-/r/`
5×	`frac-times` `associate-*r/`
4×	`insert-posit16` `add-log-exp`
3×	`clear-num` `frac-2neg` `pow-prod-down` `associate-*l/`
1×	`associate-r` `tan-quot` `*-commutative`

Counts

4 → 419

Calls

4 calls:

12.0ms	(/ (sqrt 2) (tan k))
30.0ms	(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
213.0ms	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (* (/ (sqrt 2) (tan k)) l) (sin k)) (/ (cbrt (sqrt 2)) k)))
6.0ms	(/ t (/ l k))

series1.1s

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (sqrt 2) (tan k))
410.0ms	(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k)))
625.0ms	(* (/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (/ t (/ l k))) (* (/ (* (/ (sqrt 2) (tan k)) l) (sin k)) (/ (cbrt (sqrt 2)) k)))
23.0ms	(/ t (/ l k))

simplify1.0s

Counts

431 → 431

Iterations

Iter	Nodes
1	2129
0	652

prune7.2s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0b

regimes322.0ms

Accuracy

73% (1.1b remaining)

Error of 1.1b against oracle of 0.1b and baseline of 4.0b

bsearch1.9s

Steps

Iters	Range	Point
6	1.7081301155548936e+272	1.0794451454882057e+273	1.0217052900572645e+273
10	3.846135351191654e-93	4.515285814099366e-82	1.347321606507381e-87
9	-4.0345147665861836e-72	-2.4298169582839744e-80	-1.6453940453160847e-73

Iters

Range

Point

1.7081301155548936e+272

1.0794451454882057e+273

1.0217052900572645e+273

3.846135351191654e-93

4.515285814099366e-82

1.347321606507381e-87

-4.0345147665861836e-72

-2.4298169582839744e-80

-1.6453940453160847e-73

simplify10.0ms

Iterations

Iter	Nodes
2	55
1	55
0	45

end0.0ms

sample40.5s

Algorithm

intervals

Results

12.6s	4024×	body	1280	valid
10.3s	2227×	body	2560	valid
8.8s	962×	body	5120	valid
5.7s	2594×	body	640	valid
1.3s	1031×	body	320	valid
925.0ms	2076×	body	80	valid
385.0ms	449×	body	160	valid