Details

sample927.0ms

Algorithm

intervals

Results

351.0ms	35×	body	5120	valid
204.0ms	137×	body	1280	valid
175.0ms	68×	body	2560	valid
76.0ms	77×	body	640	valid
62.0ms	62×	body	80	valid
19.0ms	28×	body	320	valid
5.0ms	10×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	3734
3	704
2	144
1	44
0	19

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 43.9b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 2.0 (pow (/ k t) 2.0))
7.4b	(/ (* l l) (* (sin k) (tan k)))
13.4b	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
33.9b	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

rewrite992.0ms

Algorithm

rewrite-expression-head

Rules

9211×	`times-frac`
3212×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
2953×	`unpow-prod-down`
656×	`div-inv`
491×	`sqr-pow`
467×	`add-exp-log`
459×	`associate-/r/`
401×	`tan-quot` `associate-*r/`
331×	`div-exp`
92×	`add-cbrt-cube`
76×	`prod-exp`
71×	`associate-/r*`
66×	`associate-/l*`
64×	`pow-exp`
50×	`cbrt-undiv`
47×	`pow-to-exp`
16×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `log1p-expm1-u` `add-log-exp`
1×	`associate-/l/`

Counts

4 → 2993

Calls

4 calls:

17.0ms	(/ 2.0 (pow (/ k t) 2.0))
23.0ms	(/ (* l l) (* (sin k) (tan k)))
34.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
160.0ms	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

series2.0s

Counts

4 → 12

Calls

4 calls:

216.0ms	(/ 2.0 (pow (/ k t) 2.0))
156.0ms	(/ (* l l) (* (sin k) (tan k)))
490.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
1.1s	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

simplify6.1s

Counts

3005 → 3005

Iterations

Iter	Nodes
done	5069
0	5069

prune37.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 14.8b

localize84.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
7.4b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
10.7b	(* (pow t 1.0) (pow k 2.0))
16.7b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite285.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`unpow2`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 608

Calls

4 calls:

27.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
25.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
29.0ms	(* (pow t 1.0) (pow k 2.0))
110.0ms	(* (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:

472.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
122.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
511.0ms	(* (pow t 1.0) (pow k 2.0))
1.1s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.4s

Counts

620 → 620

Iterations

Iter	Nodes
done	5002
2	3107
1	1170
0	445

prune1.7s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin k) l) (/ (sin k) l))
0.8b	(/ 1 (pow k 2.0))
8.1b	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l))))
16.7b	(/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l)))

rewrite388.0ms

Algorithm

rewrite-expression-head

Rules

4520×	`add-exp-log`
2317×	`div-exp`
2252×	`prod-exp`
1706×	`pow-exp`
527×	`pow-to-exp`
396×	`rec-exp` `1-exp`
112×	`add-cbrt-cube`
94×	`add-sqr-sqrt`
90×	`times-frac`
67×	`*-un-lft-identity`
64×	`add-cube-cbrt`
55×	`unpow-prod-down`
42×	`associate-l`
41×	`cbrt-undiv` `cbrt-unprod`
21×	`associate-r`
13×	`swap-sqr` `unswap-sqr`
11×	`pow1` `sqr-pow`
8×	`associate-/r*` `div-inv`
6×	`associate-/r/`
4×	`expm1-log1p-u` `associate-r/` `log1p-expm1-u` `associate-/l` `add-log-exp`
3×	`frac-times` `associate-*l/`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`pow2` `pow-plus` `pow-prod-down` `pow-sqr` `pow-prod-up` `pow-flip` `inv-pow`

Counts

4 → 1077

Calls

4 calls:

21.0ms	(* (/ (sin k) l) (/ (sin k) l))
7.0ms	(/ 1 (pow k 2.0))
143.0ms	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l))))
27.0ms	(/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (/ (sin k) l) (/ (sin k) l))
617.0ms	(/ 1 (pow k 2.0))
1.1s	(* (pow (/ 1 (pow t 1.0)) 1.0) (/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l))))
471.0ms	(/ (* (cos k) (pow (/ 1 (pow k 2.0)) 1.0)) (* (/ (sin k) l) (/ (sin k) l)))

simplify2.4s

Counts

1089 → 1089

Iterations

Iter	Nodes
done	5000
1	2291
0	843

prune2.3s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 5.7b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos k) (/ (sin k) l))
0.8b	(/ 1 (pow k 2.0))
8.2b	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
10.9b	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (cos k) (/ (sin k) l))) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

rewrite694.0ms

Algorithm

rewrite-expression-head

Rules

4909×	`add-exp-log`
3183×	`div-exp`
1966×	`pow-exp`
1948×	`times-frac`
1825×	`prod-exp`
930×	`unpow-prod-down`
881×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
607×	`pow-to-exp`
456×	`rec-exp` `1-exp`
382×	`associate-r`
112×	`sqr-pow`
94×	`div-inv`
70×	`add-cbrt-cube`
35×	`associate-/l*`
33×	`associate-/r*`
28×	`cbrt-undiv`
21×	`cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-*r/` `associate-/r/`
1×	`frac-times` `associate-l` `pow-prod-down` `associate-l/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1919

Calls

4 calls:

16.0ms	(/ (cos k) (/ (sin k) l))
7.0ms	(/ 1 (pow k 2.0))
50.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
227.0ms	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (cos k) (/ (sin k) l))) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

series2.3s

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (cos k) (/ (sin k) l))
539.0ms	(/ 1 (pow k 2.0))
486.0ms	(/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l))
1.1s	(* (* (pow (/ 1 (pow t 1.0)) 1.0) (/ (cos k) (/ (sin k) l))) (/ (pow (/ 1 (pow k 2.0)) 1.0) (/ (sin k) l)))

simplify3.5s

Counts

1931 → 1931

Iterations

Iter	Nodes
done	5000
0	1878

prune10.3s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 0.0b

regimes872.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	31
1	31
0	24

end0.0ms

sample28.6s

Algorithm

intervals

Results

8.4s	4151×	body	1280	valid
7.8s	2136×	body	2560	valid
6.0s	925×	body	5120	valid
3.4s	2536×	body	640	valid
1.4s	1977×	body	80	valid
802.0ms	994×	body	320	valid
227.0ms	454×	body	160	valid