Details

sample996.0ms

Algorithm

intervals

Results

322.0ms	125×	body	1280	valid
272.0ms	42×	body	5120	valid
247.0ms	80×	body	2560	valid
79.0ms	83×	body	640	valid
21.0ms	34×	body	320	valid
13.0ms	60×	body	80	valid
7.0ms	14×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.0b

localize80.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
0.4b	(* (pow (/ k t) 2.0) (tan k))
14.0b	(/ (pow t 3.0) (/ l (/ (sin k) l)))
34.0b	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

rewrite1.3s

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:

121.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
24.0ms	(* (pow (/ k t) 2.0) (tan k))
52.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
419.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

series2.0s

Counts

4 → 12

Calls

4 calls:

499.0ms	(/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l))))
380.0ms	(* (pow (/ k t) 2.0) (tan k))
360.0ms	(/ (pow t 3.0) (/ l (/ (sin k) l)))
747.0ms	(/ (/ 2.0 (/ (pow t 3.0) (/ l (/ (sin k) l)))) (* (pow (/ k t) 2.0) (tan k)))

simplify5.2s

Counts

3678 → 3678

Iterations

Iter	Nodes
done	5342
0	5342

prune43.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 16.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.7b	(* (pow t 1.0) (pow k 2.0))
16.5b	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite229.0ms

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:

20.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
14.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
18.0ms	(* (pow t 1.0) (pow k 2.0))
119.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts

4 → 12

Calls

4 calls:

611.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
146.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
499.0ms	(* (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)))

simplify4.9s

Counts

612 → 612

Iterations

Iter	Nodes
done	5000
1	1217
0	437

prune1.5s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 11.2b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.7b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
5.2b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.5b	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite519.0ms

Algorithm

rewrite-expression-head

Rules

5603×	`add-exp-log`
4515×	`prod-exp`
3078×	`pow-exp`
2032×	`div-exp`
1869×	`pow-to-exp`
434×	`rec-exp` `1-exp`
27×	`add-cbrt-cube`
23×	`add-sqr-sqrt`
22×	`times-frac`
20×	`unpow-prod-down`
18×	`*-un-lft-identity` `add-cube-cbrt`
12×	`associate-r`
11×	`associate-l`
9×	`associate-/r*`
8×	`cbrt-unprod`
7×	`cbrt-undiv`
6×	`pow1` `sqr-pow`
4×	`div-inv` `associate-/l*` `unpow2` `add-log-exp`
3×	`pow-unpow` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-r/` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

5.0ms	(pow (sin k) 2)
74.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
23.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
148.0ms	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.8s

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow (sin k) 2)
586.0ms	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
126.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.0s	(* (pow (/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify5.4s

Counts

1472 → 1472

Iterations

Iter	Nodes
done	5000
1	1741
0	574

prune1.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.7b

localize96.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
0.6b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
6.6b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))))
10.0b	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

13823×	`add-exp-log`
8491×	`prod-exp`
6385×	`div-exp`
6247×	`pow-exp`
2221×	`pow-to-exp`
1352×	`rec-exp` `1-exp`
85×	`add-cbrt-cube`
64×	`add-sqr-sqrt`
59×	`unpow-prod-down`
54×	`times-frac`
40×	`associate-l`
34×	`*-un-lft-identity`
32×	`cbrt-unprod`
29×	`cbrt-undiv`
28×	`add-cube-cbrt`
18×	`unswap-sqr`
11×	`associate-r` `sqr-pow`
6×	`associate-/r/` `associate-/l*`
5×	`pow1` `associate-*r/` `div-inv`
4×	`add-log-exp`
2×	`frac-times` `clear-num` `associate-/r` `frac-2neg` `associate-l/` `*-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 2662

Calls

4 calls:

29.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
20.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
115.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))))
249.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))
485.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
447.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l))))
1.0s	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (/ (cos k) (* (/ (sin k) l) (/ (sin k) l)))))

simplify4.8s

Counts

2674 → 2674

Iterations

Iter	Nodes
done	5000
1	4218
0	1260

prune1.8s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 5.4b

regimes1.2s

Accuracy

8.5% (4.4b remaining)

Error of 9.0b against oracle of 4.6b and baseline of 9.4b

bsearch3.0ms

simplify12.0ms

Iterations

Iter	Nodes
done	59
1	59
0	44

end0.0ms

sample30.4s

Algorithm

intervals

Results

9.6s	2317×	body	2560	valid
8.3s	3989×	body	1280	valid
6.5s	932×	body	5120	valid
3.2s	2554×	body	640	valid
1.2s	977×	body	320	valid
679.0ms	1985×	body	80	valid
232.0ms	421×	body	160	valid