Details

sample638.0ms

Algorithm

intervals

Results

165.0ms	34×	body	5120	valid
160.0ms	71×	body	2560	valid
159.0ms	130×	body	1280	valid
89.0ms	81×	body	640	valid
20.0ms	43×	body	320	valid
9.0ms	58×	body	80	valid
6.0ms	19×	body	160	valid

simplify812.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	856
2	149
1	44
0	19

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 36.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
4.0b	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
5.9b	(* (pow t 3.0) (/ (sin k) l))
29.8b	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

569×	`times-frac`
499×	`add-exp-log`
286×	`div-exp`
275×	`add-sqr-sqrt`
230×	`unpow-prod-down`
229×	`*-un-lft-identity` `add-cube-cbrt`
150×	`prod-exp`
147×	`associate-l`
77×	`add-cbrt-cube`
76×	`pow-exp`
57×	`div-inv`
52×	`pow-to-exp`
38×	`associate-*r/`
37×	`associate-/r/`
34×	`cbrt-undiv`
27×	`associate-r`
22×	`sqr-pow`
20×	`cbrt-unprod`
18×	`associate-/r*`
16×	`unswap-sqr`
11×	`associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `*-commutative`
1×	`frac-times` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/l/`

Counts

4 → 539

Calls

4 calls:

10.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
109.0ms	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
16.0ms	(* (pow t 3.0) (/ (sin k) l))
45.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

series2.4s

Counts

4 → 12

Calls

4 calls:

418.0ms	(/ 2.0 (* (pow t 3.0) (/ (sin k) l)))
1.1s	(* (/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0)) (/ l (tan k)))
309.0ms	(* (pow t 3.0) (/ (sin k) l))
612.0ms	(/ (/ 2.0 (* (pow t 3.0) (/ (sin k) l))) (pow (/ k t) 2.0))

simplify1.1s

Counts

551 → 551

Iterations

Iter	Nodes
done	5001
1	2527
0	795

prune3.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.3b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ l (sin k))
4.0b	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
6.2b	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
7.5b	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))

rewrite1.2s

Algorithm

rewrite-expression-head

Rules

1087×	`add-exp-log`
540×	`prod-exp`
508×	`div-exp`
370×	`times-frac`
319×	`pow-exp`
190×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
150×	`unpow-prod-down`
139×	`pow-to-exp`
64×	`add-cbrt-cube`
63×	`rec-exp` `1-exp`
50×	`sqr-pow`
28×	`cbrt-unprod` `associate-/l*`
27×	`associate-r`
15×	`cbrt-undiv`
12×	`div-inv`
11×	`pow1`
10×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-l` `*-commutative`
1×	`frac-times` `associate-*l/` `tan-quot` `associate-/r/` `associate-/l/`

Counts

4 → 557

Calls

4 calls:

9.0ms	(/ l (sin k))
868.0ms	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
26.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
213.0ms	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))

series2.7s

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ l (sin k))
1.1s	(* (* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k))) (/ l (tan k)))
830.0ms	(/ (/ 1 (pow t 1.0)) (pow k 2.0))
667.0ms	(* (* 2.0 (pow (/ (/ 1 (pow t 1.0)) (pow k 2.0)) 1.0)) (/ l (sin k)))

simplify1.5s

Counts

569 → 569

Iterations

Iter	Nodes
done	5000
1	2190
0	762

prune2.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 5.8b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
0.2b	(* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))))
4.0b	(* (* (* 2.0 (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0)) (/ l (sin k))) (/ l (tan k)))
7.5b	(* (* 2.0 (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0)) (/ l (sin k)))

rewrite1.1s

Algorithm

rewrite-expression-head

Rules

12405×	`add-exp-log`
7190×	`prod-exp`
6281×	`div-exp`
3866×	`pow-exp`
2006×	`pow-to-exp`
1290×	`rec-exp` `1-exp`
1109×	`times-frac`
794×	`add-sqr-sqrt`
474×	`*-un-lft-identity`
432×	`unpow-prod-down`
345×	`add-cube-cbrt`
234×	`sqr-pow`
206×	`associate-r`
154×	`unswap-sqr`
83×	`add-cbrt-cube`
34×	`cbrt-unprod`
27×	`associate-l`
25×	`associate-/l*`
23×	`cbrt-undiv`
20×	`div-inv`
13×	`pow1`
7×	`associate-/r*`
5×	`pow-prod-down` `associate-*r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`frac-times` `associate-*l/`
1×	`clear-num` `frac-2neg` `tan-quot` `associate-/r/` `associate-/l/`

Counts

4 → 2896

Calls

4 calls:

23.0ms	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
189.0ms	(* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))))
199.0ms	(* (* (* 2.0 (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0)) (/ l (sin k))) (/ l (tan k)))
101.0ms	(* (* 2.0 (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0)) (/ l (sin k)))

series2.8s

Counts

4 → 12

Calls

4 calls:

514.0ms	(/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))
559.0ms	(* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))))
1.1s	(* (* (* 2.0 (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0)) (/ l (sin k))) (/ l (tan k)))
640.0ms	(* (* 2.0 (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0)) (/ l (sin k)))

simplify1.5s

Counts

2908 → 2908

Iterations

Iter	Nodes
done	5001
0	1985

prune7.6s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 5.8b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))))
0.3b	(/ (* 2.0 (* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)) (sin k))
4.0b	(* (/ (* 2.0 (* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)) (sin k)) (/ l (tan k)))
8.2b	(* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)

rewrite919.0ms

Algorithm

rewrite-expression-head

Rules

8207×	`add-exp-log`
4591×	`div-exp`
4376×	`prod-exp`
2659×	`pow-exp`
1419×	`pow-to-exp`
915×	`rec-exp` `1-exp`
764×	`times-frac`
637×	`add-sqr-sqrt`
309×	`*-un-lft-identity`
283×	`unpow-prod-down`
196×	`associate-r`
186×	`sqr-pow`
180×	`add-cube-cbrt`
158×	`unswap-sqr`
68×	`add-cbrt-cube`
37×	`associate-l`
24×	`cbrt-unprod`
22×	`cbrt-undiv`
12×	`div-inv`
8×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `-commutative`
2×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/`
1×	`clear-num` `frac-2neg` `tan-quot` `associate-/r/` `associate-/l*`

Counts

4 → 2036

Calls

4 calls:

169.0ms	(* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))))
109.0ms	(/ (* 2.0 (* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)) (sin k))
161.0ms	(* (/ (* 2.0 (* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)) (sin k)) (/ l (tan k)))
47.0ms	(* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)

series3.0s

Counts

4 → 12

Calls

4 calls:

455.0ms	(* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2))))
1.0s	(/ (* 2.0 (* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)) (sin k))
1.1s	(* (/ (* 2.0 (* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)) (sin k)) (/ l (tan k)))
512.0ms	(* (pow (* (/ 1 (pow k (/ 2.0 2))) (/ (/ 1 (pow t 1.0)) (pow k (/ 2.0 2)))) 1.0) l)

simplify1.3s

Counts

2048 → 2048

Iterations

Iter	Nodes
done	5000
0	1626

prune5.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 4.0b

regimes816.0ms

Accuracy

0% (2.1b remaining)

Error of 5.8b against oracle of 3.7b and baseline of 5.8b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	29
1	29
0	23

end0.0ms

sample31.6s

Algorithm

intervals

Results

9.0s	4074×	body	1280	valid
8.6s	2308×	body	2560	valid
7.4s	920×	body	5120	valid
3.5s	2532×	body	640	valid
1.5s	1028×	body	320	valid
525.0ms	2095×	body	80	valid
296.0ms	447×	body	160	valid