Details

sample798.0ms

Algorithm

intervals

Results

219.0ms	138×	body	1280	valid
204.0ms	26×	body	5120	valid
176.0ms	67×	body	2560	valid
74.0ms	85×	body	640	valid
67.0ms	34×	body	320	valid
13.0ms	69×	body	80	valid
4.0ms	10×	body	160	valid

simplify6.2s

Counts

1 → 1

Iterations

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

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize91.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin k) (tan k))
5.1b	(/ (* l l) (* (sin k) (tan k)))
14.3b	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
30.6b	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

rewrite1.5s

Algorithm

rewrite-expression-head

Rules

9124×	`times-frac`
3166×	`add-sqr-sqrt`
3164×	`*-un-lft-identity` `add-cube-cbrt`
2901×	`unpow-prod-down`
651×	`div-inv`
487×	`sqr-pow`
461×	`add-exp-log`
459×	`associate-/r/`
402×	`tan-quot` `associate-*r/`
326×	`div-exp`
92×	`add-cbrt-cube`
77×	`prod-exp`
63×	`associate-/l*`
62×	`pow-exp`
54×	`associate-/r*`
49×	`cbrt-undiv`
46×	`pow-to-exp`
17×	`cbrt-unprod`
6×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-r` `associate-l`
1×	`pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 2930

Calls

4 calls:

19.0ms	(* (sin k) (tan k))
21.0ms	(/ (* l l) (* (sin k) (tan k)))
55.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
205.0ms	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

series3.4s

Counts

4 → 12

Calls

4 calls:

130.0ms	(* (sin k) (tan k))
378.0ms	(/ (* l l) (* (sin k) (tan k)))
859.0ms	(/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k))))
2.0s	(/ (/ 2.0 (pow (/ k t) 2.0)) (/ (pow t 3.0) (/ (* l l) (* (sin k) (tan k)))))

simplify9.8s

Counts

2942 → 2942

Iterations

Iter	Nodes
done	5074
0	5074

prune59.4s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 11.1b

localize106.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* (pow t 1.0) (pow k 2.0)))
5.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
8.1b	(* (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)))

rewrite381.0ms

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` `insert-posit16` `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 → 612

Calls

4 calls:

24.0ms	(/ 1 (* (pow t 1.0) (pow k 2.0)))
31.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
41.0ms	(* (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)))

series4.8s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ 1 (* (pow t 1.0) (pow k 2.0)))
254.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.3s	(* (pow t 1.0) (pow k 2.0))
2.0s	(* (pow (/ 1 (* (pow t 1.0) (pow k 2.0))) 1.0) (/ (* (cos k) (pow l 2)) (pow (sin k) 2)))

simplify8.7s

Counts

624 → 624

Iterations

Iter	Nodes
done	5015
2	3082
1	1169
0	449

prune2.8s

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 7.2b

localize105.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin k) 2)
0.6b	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
5.1b	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
16.7b	(* (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)))

rewrite1.0s

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 1472

Calls

4 calls:

11.0ms	(pow (sin k) 2)
141.0ms	(/ 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))
310.0ms	(* (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)))

series3.6s

Counts

4 → 12

Calls

4 calls:

55.0ms	(pow (sin k) 2)
1.3s	(/ 1 (* (* (pow t 1.0) (pow k (/ 2.0 2))) (pow k (/ 2.0 2))))
282.0ms	(/ (* (cos k) (pow l 2)) (pow (sin k) 2))
1.9s	(* (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)))

simplify8.2s

Counts

1484 → 1484

Iterations

Iter	Nodes
done	5002
2	3536
1	1610
0	586

prune2.7s

Pruning

27 alts after pruning (27 fresh and 0 done)

Merged error: 6.2b

localize165.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
5.1b	(/ (* l l) (/ (* (sin k) (sin k)) (cos k)))
6.5b	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (/ (* l l) (/ (* (sin k) (sin k)) (cos k))) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))
8.3b	(* (/ (* l l) (/ (* (sin k) (sin k)) (cos k))) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))

rewrite2.3s

Algorithm

rewrite-expression-head

Rules

16036×	`add-exp-log`
10028×	`prod-exp`
7277×	`pow-exp`
7238×	`div-exp`
2585×	`pow-to-exp`
1574×	`rec-exp` `1-exp`
97×	`add-cbrt-cube`
95×	`times-frac`
85×	`add-sqr-sqrt`
68×	`unpow-prod-down`
40×	`*-un-lft-identity`
38×	`cbrt-unprod`
32×	`cbrt-undiv`
31×	`add-cube-cbrt`
30×	`associate-r`
27×	`unswap-sqr`
23×	`associate-l`
14×	`sqr-pow`
8×	`associate-/r*` `div-inv`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l/` `associate-/r/` `-commutative`
1×	`associate-*r/` `pow-flip` `inv-pow`

Counts

4 → 3103

Calls

4 calls:

33.0ms	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
25.0ms	(/ (* l l) (/ (* (sin k) (sin k)) (cos k)))
425.0ms	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (/ (* l l) (/ (* (sin k) (sin k)) (cos k))) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))
172.0ms	(* (/ (* l l) (/ (* (sin k) (sin k)) (cos k))) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))

series4.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(/ 1 (* (pow t 1.0) (pow k (/ 2.0 2))))
216.0ms	(/ (* l l) (/ (* (sin k) (sin k)) (cos k)))
1.7s	(* (pow (/ 1 (* (pow t 1.0) (pow k (/ 2.0 2)))) 1.0) (* (/ (* l l) (/ (* (sin k) (sin k)) (cos k))) (pow (/ 1 (pow k (/ 2.0 2))) 1.0)))
774.0ms	(* (/ (* l l) (/ (* (sin k) (sin k)) (cos k))) (pow (/ 1 (pow k (/ 2.0 2))) 1.0))

simplify10.8s

Counts

3115 → 3115

Iterations

Iter	Nodes
done	5000
1	4284
0	1481

prune3.5s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 2.0b

regimes2.4s

Accuracy

0% (5.7b remaining)

Error of 9.4b against oracle of 3.7b and baseline of 9.4b

bsearch0.0ms

simplify11.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample31.4s

Algorithm

intervals

Results

10.2s	2252×	body	2560	valid
7.4s	992×	body	5120	valid
7.2s	4083×	body	1280	valid
4.0s	2539×	body	640	valid
796.0ms	993×	body	320	valid
659.0ms	1986×	body	80	valid
301.0ms	430×	body	160	valid