Details

sample832.0ms

Algorithm

intervals

Results

250.0ms	32×	body	5120	valid
212.0ms	66×	body	2560	valid
190.0ms	119×	body	1280	valid
89.0ms	94×	body	640	valid
24.0ms	30×	body	320	valid
15.0ms	72×	body	80	valid
7.0ms	17×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 4 (1.5s)

Iter	Nodes	Cost
0	19	25
1	44	25
2	146	25
3	798	23
4	4467	21
done	5000	21

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 44.8b

localize37.0ms

Local error

Found 4 expressions with local error:

0.8b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
1.0b	(* (/ (pow t 3.0) (* l l)) (sin k))
16.2b	(/ (pow t 3.0) (* l l))
31.8b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite392.0ms

Algorithm

rewrite-expression-head

Rules

340×	`times-frac`
272×	`add-exp-log`
153×	`unpow-prod-down`
144×	`add-sqr-sqrt`
137×	`add-cube-cbrt` `*-un-lft-identity`
128×	`div-exp`
103×	`prod-exp`
59×	`add-cbrt-cube`
58×	`associate-*l/`
54×	`associate-/r/`
38×	`tan-quot`
34×	`pow-exp`
32×	`div-inv`
24×	`pow-to-exp`
21×	`cbrt-unprod`
19×	`cbrt-undiv` `frac-times` `associate-*r/`
18×	`associate-/r*`
17×	`associate-/l*`
15×	`sqr-pow`
12×	`associate-l`
11×	`pow1`
6×	`associate-r`
4×	`pow-prod-down` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 354

Calls

4 calls:

123.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
56.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
18.0ms	(/ (pow t 3.0) (* l l))
168.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.9s

Counts

4 → 12

Calls

4 calls:

421.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
325.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
290.0ms	(/ (pow t 3.0) (* l l))
886.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify1.0s

Counts

366 → 366

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	662	10242
1	1504	9739
done	5001	9233

prune2.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 16.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow k 2.0) (pow t 1.0)))
5.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.9b	(* (pow k 2.0) (pow t 1.0))
17.0b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite292.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 600

Calls

4 calls:

23.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
35.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
35.0ms	(* (pow k 2.0) (pow t 1.0))
112.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.3s

Counts

4 → 12

Calls

4 calls:

563.0ms	(/ 1 (* (pow k 2.0) (pow t 1.0)))
137.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
482.0ms	(* (pow k 2.0) (pow t 1.0))
1.1s	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify1.9s

Counts

612 → 612

Iterations

Useful iterations: 2 (790.0ms)

Iter	Nodes	Cost
0	483	15017
1	1096	13295
2	2840	12595
done	5000	12595

prune926.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.5b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.7b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
5.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite682.0ms

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×	`add-cube-cbrt` `*-un-lft-identity`
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×	`frac-2neg` `clear-num`
1×	`pow-flip` `pow-pow` `associate-r/` `-commutative` `inv-pow`

Counts

4 → 1460

Calls

4 calls:

4.0ms	(pow (sin k) 2)
78.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
25.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
276.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series2.2s

Counts

4 → 12

Calls

4 calls:

32.0ms	(pow (sin k) 2)
1.0s	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
128.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
993.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify2.0s

Counts

1472 → 1472

Iterations

Useful iterations: 2 (875.0ms)

Iter	Nodes	Cost
0	597	50343
1	1262	33112
2	2940	31574
done	5000	31574

prune1.0s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.4b

localize56.0ms

Local error

Found 4 expressions with local error:

0.8b	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
4.0b	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
5.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.5b	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

rewrite2.1s

Algorithm

rewrite-expression-head

Rules

25023×	`add-exp-log`
19197×	`prod-exp`
16899×	`pow-exp`
11140×	`div-exp`
7959×	`pow-to-exp`
2990×	`rec-exp` `1-exp`
51×	`unpow-prod-down`
43×	`times-frac`
41×	`associate-l`
37×	`add-cbrt-cube`
36×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cbrt-unprod`
12×	`associate-r`
9×	`associate-/r*` `sqr-pow`
8×	`cbrt-undiv`
5×	`pow1` `div-inv`
4×	`associate-/l*` `add-log-exp`
3×	`unpow2` `unswap-sqr`
2×	`frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `associate-*r/` `inv-pow`

Counts

4 → 5762

Calls

4 calls:

29.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
340.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
18.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
122.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

series1.8s

Counts

4 → 12

Calls

4 calls:

471.0ms	(/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0)))
641.0ms	(* (pow (/ 1 (pow k (/ 2.0 2))) 1.0) (* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0)))
144.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
578.0ms	(* (/ (* (cos k) (pow l 2)) (pow (sin k) 2)) (pow (/ 1 (* (pow k (/ 2.0 2)) (pow t 1.0))) 1.0))

simplify3.5s

Counts

5774 → 5774

Iterations

Useful iterations: 2 (2.0s)

Iter	Nodes	Cost
0	1477	226017
1	2412	201321
2	4559	190075
done	5001	190075

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.5b

regimes623.0ms

Accuracy

26.4% (4.3b remaining)

Error of 14.3b against oracle of 10.0b and baseline of 15.9b

bsearch1.5s

Steps

Iters	Range		Point
5	2.1675125417143413e+135	5.369016605326505e+135	5.307433067528376e+135
9	-2.0545059602165346e+153	-1.123814921454156e+146	-2.0150601778123175e+153

simplify14.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	53	110
1	65	110
done	65	110

end0.0ms

sample30.9s

Algorithm

intervals

Results

9.6s	4014×	body	1280	valid
8.6s	2225×	body	2560	valid
6.2s	898×	body	5120	valid
3.3s	2521×	body	640	valid
1.2s	2013×	body	80	valid
864.0ms	1058×	body	320	valid
220.0ms	454×	body	160	valid