Details

sample894.0ms

Algorithm

intervals

Results

256.0ms	32×	body	5120	valid
232.0ms	71×	body	2560	valid
177.0ms	125×	body	1280	valid
80.0ms	72×	body	80	valid
74.0ms	79×	body	640	valid
24.0ms	38×	body	320	valid
7.0ms	18×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	832
2	147
1	44
0	19

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.6b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
0.8b	(* (pow (/ k t) 2.0) (tan k))
16.0b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
30.2b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

12307×	`times-frac`
4673×	`add-sqr-sqrt`
4665×	`*-un-lft-identity` `add-cube-cbrt`
1470×	`unpow-prod-down`
954×	`associate-/l*`
487×	`sqr-pow`
358×	`associate-/r*`
350×	`add-exp-log`
328×	`div-inv`
253×	`div-exp`
93×	`associate-/r/`
74×	`add-cbrt-cube`
48×	`prod-exp`
46×	`cbrt-undiv`
45×	`pow-exp`
33×	`pow-to-exp`
17×	`associate-l`
6×	`cbrt-unprod`
4×	`pow1` `add-log-exp` `unswap-sqr`
3×	`clear-num` `frac-2neg` `associate-r`
2×	`tan-quot` `associate-*r/`
1×	`*-commutative` `associate-/l/`

Counts

4 → 3666

Calls

4 calls:

129.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
23.0ms	(* (pow (/ k t) 2.0) (tan k))
49.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
392.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series1.7s

Counts

4 → 12

Calls

4 calls:

353.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
249.0ms	(* (pow (/ k t) 2.0) (tan k))
338.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
746.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify4.9s

Counts

3678 → 3678

Iterations

Iter	Nodes
done	5342
0	5342

prune44.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
6.3b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.4b	(* (pow t 1.0) (pow k 2.0))
15.0b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
1122×	`prod-exp`
899×	`pow-exp`
688×	`div-exp`
509×	`pow-to-exp`
140×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
29×	`unpow-prod-down`
25×	`add-cbrt-cube`
22×	`times-frac`
20×	`*-un-lft-identity` `add-cube-cbrt`
19×	`associate-r`
18×	`associate-l`
13×	`sqr-pow`
12×	`unswap-sqr`
9×	`associate-/r*`
7×	`cbrt-unprod`
6×	`cbrt-undiv`
5×	`pow1`
4×	`div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 600

Calls

4 calls:

19.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
13.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
13.0ms	(* (pow t 1.0) (pow k 2.0))
118.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

504.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
117.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
558.0ms	(* (pow t 1.0) (pow k 2.0))
973.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify4.4s

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1217
0	437

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.0b

localize65.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.8b	(/ 1 (pow k 2.0))
7.3b	(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (* (/ (sin k) l) (/ (sin k) l)) (cos k))))
10.5b	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (* (/ (sin k) l) (/ (sin k) l)) (cos k)))

rewrite698.0ms

Algorithm

rewrite-expression-head

Rules

2600×	`add-exp-log`
1741×	`div-exp`
1640×	`times-frac`
1142×	`add-sqr-sqrt`
1049×	`unpow-prod-down`
914×	`pow-exp`
778×	`prod-exp`
549×	`*-un-lft-identity`
420×	`add-cube-cbrt`
317×	`pow-to-exp`
232×	`unswap-sqr`
221×	`associate-r`
219×	`sqr-pow`
135×	`sqrt-prod`
129×	`rec-exp` `1-exp`
82×	`div-inv`
76×	`add-cbrt-cube`
63×	`associate-l`
35×	`cbrt-undiv`
32×	`associate-/l*`
19×	`cbrt-unprod`
14×	`associate-/r*`
13×	`swap-sqr`
11×	`pow1`
4×	`add-log-exp`
2×	`clear-num` `frac-2neg` `associate-r/` `associate-/r/` `-commutative`
1×	`pow2` `frac-times` `pow-plus` `pow-prod-down` `associate-*l/` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 1388

Calls

4 calls:

25.0ms	(* (/ (sin k) l) (/ (sin k) l))
10.0ms	(/ 1 (pow k 2.0))
392.0ms	(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (* (/ (sin k) l) (/ (sin k) l)) (cos k))))
75.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (* (/ (sin k) l) (/ (sin k) l)) (cos k)))

series2.1s

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (/ (sin k) l) (/ (sin k) l))
553.0ms	(/ 1 (pow k 2.0))
1.0s	(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (* (/ (sin k) l) (/ (sin k) l)) (cos k))))
445.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (* (/ (sin k) l) (/ (sin k) l)) (cos k)))

simplify2.9s

Counts

1400 → 1400

Iterations

Iter	Nodes
done	5001
1	4570
0	1440

prune9.0s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 0.1b

localize88.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (sin k) l) (cos k))
0.3b	(/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1))
0.3b	(/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) (cos k)))
4.8b	(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1)))

rewrite4.1s

Algorithm

rewrite-expression-head

Rules

24774×	`times-frac`
12065×	`add-sqr-sqrt`
10021×	`unpow-prod-down`
9714×	`*-un-lft-identity`
9063×	`add-cube-cbrt`
3498×	`sqrt-prod`
2155×	`associate-r`
1408×	`sqr-pow`
912×	`add-exp-log`
748×	`div-inv`
732×	`unswap-sqr`
708×	`div-exp`
345×	`pow-exp`
186×	`prod-exp`
138×	`pow-to-exp`
113×	`associate-/l*`
89×	`associate-/r*`
84×	`1-exp`
50×	`associate-l`
41×	`add-cbrt-cube`
21×	`cbrt-undiv`
4×	`pow1` `cbrt-unprod` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/r/`
1×	`associate-r/` `-commutative` `associate-/l/`

Counts

4 → 7768

Calls

4 calls:

23.0ms	(/ (/ (sin k) l) (cos k))
127.0ms	(/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1))
91.0ms	(/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) (cos k)))
2.2s	(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1)))

series1.5s

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (/ (sin k) l) (cos k))
411.0ms	(/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1))
423.0ms	(/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) (cos k)))
627.0ms	(* (pow (/ (sqrt 1) (pow t 1.0)) 1.0) (/ (pow (/ (sqrt 1) (pow k (/ 2.0 2))) 1.0) (/ (/ (sin k) l) 1)))

simplify10.0s

Counts

7780 → 7780

Iterations

Iter	Nodes
done	8384
0	8384

prune1.7m

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes574.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample23.7s

Algorithm

intervals

Results

6.8s	2196×	body	2560	valid
5.9s	952×	body	5120	valid
5.9s	4025×	body	1280	valid
3.3s	2527×	body	640	valid
538.0ms	947×	body	320	valid
380.0ms	2009×	body	80	valid
150.0ms	437×	body	160	valid