Details

sample440.0ms

Algorithm

intervals

Results

141.0ms	38×	body	5120	valid
123.0ms	71×	body	2560	valid
95.0ms	119×	body	1280	valid
33.0ms	67×	body	640	valid
11.0ms	33×	body	320	valid
9.0ms	81×	body	80	valid
3.0ms	14×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Useful iterations: 4 (975.0ms)

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

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
0.8b	(* (/ (pow t 3.0) (* l l)) (sin k))
16.9b	(/ (pow t 3.0) (* l l))
26.9b	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

rewrite245.0ms

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:

72.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
31.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
12.0ms	(/ (pow t 3.0) (* l l))
104.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

series1.4s

Counts

4 → 12

Calls

4 calls:

327.0ms	(* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))
253.0ms	(* (/ (pow t 3.0) (* l l)) (sin k))
185.0ms	(/ (pow t 3.0) (* l l))
592.0ms	(/ (/ 2.0 (* (* (/ (pow t 3.0) (* l l)) (sin k)) (tan k))) (pow (/ k t) 2.0))

simplify649.0ms

Counts

366 → 366

Iterations

Useful iterations: done (634.0ms)

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

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 14.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
5.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
7.1b	(* (pow k 2.0) (pow t 1.0))
12.9b	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

rewrite166.0ms

Algorithm

rewrite-expression-head

Rules

1597×	`add-exp-log`
1095×	`prod-exp`
882×	`pow-exp`
668×	`div-exp`
492×	`pow-to-exp`
130×	`rec-exp` `1-exp`
37×	`add-sqr-sqrt`
32×	`unpow-prod-down`
20×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
19×	`times-frac` `associate-r`
18×	`associate-l`
14×	`sqr-pow`
12×	`unswap-sqr`
8×	`associate-/r*`
6×	`cbrt-unprod`
5×	`pow1`
4×	`cbrt-undiv` `unpow2` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 567

Calls

4 calls:

3.0ms	(pow (sin k) 2)
15.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
17.0ms	(* (pow k 2.0) (pow t 1.0))
69.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

series1.3s

Counts

4 → 12

Calls

4 calls:

23.0ms	(pow (sin k) 2)
85.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
328.0ms	(* (pow k 2.0) (pow t 1.0))
844.0ms	(* (pow (/ 1 (* (pow k 2.0) (pow t 1.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify972.0ms

Counts

579 → 579

Iterations

Useful iterations: 2 (407.0ms)

Iter	Nodes	Cost
0	438	14412
1	949	12754
2	2545	12085
done	5000	12085

prune596.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos k) (pow l 2))
0.4b	(pow (sin k) 2)
5.5b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
12.9b	(* (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)))

rewrite378.0ms

Algorithm

rewrite-expression-head

Rules

5397×	`add-exp-log`
4347×	`prod-exp`
2995×	`pow-exp`
1970×	`div-exp`
1786×	`pow-to-exp`
403×	`rec-exp` `1-exp`
30×	`add-sqr-sqrt`
24×	`unpow-prod-down`
20×	`associate-r` `add-cbrt-cube`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
14×	`associate-l`
8×	`associate-/r*` `sqr-pow`
7×	`unswap-sqr`
6×	`cbrt-unprod` `unpow2`
5×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`pow-unpow` `div-inv`
2×	`*-commutative`
1×	`pow-pow` `frac-2neg` `associate-r/` `clear-num` `associate-/l`

Counts

4 → 1372

Calls

4 calls:

13.0ms	(* (cos k) (pow l 2))
3.0ms	(pow (sin k) 2)
16.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
131.0ms	(* (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)))

series820.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (cos k) (pow l 2))
24.0ms	(pow (sin k) 2)
86.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
664.0ms	(* (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)))

simplify1.1s

Counts

1384 → 1384

Iterations

Useful iterations: 2 (530.0ms)

Iter	Nodes	Cost
0	554	48096
1	1093	32072
2	2518	30567
done	5000	30567

prune590.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
2.4b	(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
3.0b	(/ (pow l 2) (sin k))
12.9b	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

rewrite399.0ms

Algorithm

rewrite-expression-head

Rules

4561×	`add-exp-log`
3350×	`prod-exp`
1881×	`pow-exp`
1593×	`div-exp`
1044×	`pow-to-exp`
310×	`rec-exp` `1-exp`
77×	`add-sqr-sqrt`
76×	`times-frac`
48×	`add-cube-cbrt` `*-un-lft-identity`
45×	`add-cbrt-cube`
30×	`unpow-prod-down`
29×	`associate-r`
24×	`associate-l`
16×	`cbrt-unprod`
12×	`cbrt-undiv`
11×	`associate-/l*`
10×	`unswap-sqr` `sqr-pow`
9×	`unpow2`
7×	`pow1`
5×	`associate-*r/` `div-inv`
4×	`associate-/r*` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-l/` `clear-num` `-commutative`
1×	`pow-flip` `pow-prod-down` `inv-pow`

Counts

4 → 1131

Calls

4 calls:

45.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
35.0ms	(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
10.0ms	(/ (pow l 2) (sin k))
138.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

series1.2s

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0))))
91.0ms	(* (/ (cos k) (sin k)) (/ (pow l 2) (sin k)))
52.0ms	(/ (pow l 2) (sin k))
668.0ms	(* (pow (/ 1 (* (pow k (/ 2.0 2)) (* (pow k (/ 2.0 2)) (pow t 1.0)))) 1.0) (* (/ (cos k) (sin k)) (/ (pow l 2) (sin k))))

simplify1.6s

Counts

1143 → 1143

Iterations

Useful iterations: 2 (847.0ms)

Iter	Nodes	Cost
0	675	38489
1	1434	25713
2	3519	23406
done	5001	23406

prune757.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.6b

regimes466.0ms

Accuracy

23.8% (5.2b remaining)

Error of 14.6b against oracle of 9.4b and baseline of 16.2b

bsearch3.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	73
1	51	73
done	51	73

end0.0ms

sample14.5s

Algorithm

intervals

Results

4.4s	2257×	body	2560	valid
4.3s	992×	body	5120	valid
3.2s	4014×	body	1280	valid
1.3s	2448×	body	640	valid
358.0ms	1042×	body	320	valid
258.0ms	2087×	body	80	valid
120.0ms	474×	body	160	valid