Details

sample69.0ms

Algorithm

intervals

Results

34.0ms	61×	body	1280	valid
11.0ms	36×	body	640	valid
8.0ms	135×	body	80	valid
4.0ms	18×	body	320	valid
1.0ms	6×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9
done	288	9

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.9b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`times-frac`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r`
5×	`associate-*l/`
4×	`pow-prod-down`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/l/` `associate-/l*`

Counts

3 → 85

Calls

3 calls:

65.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
27.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
67.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series194.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
47.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
85.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify71.0ms

Counts

94 → 94

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	412	862
1	2127	656
2	5001	637
done	5001	637

prune286.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
28×	`times-frac`
26×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-r`
14×	`associate-l`
12×	`prod-exp` `cbrt-unprod`
10×	`pow1`
7×	`cbrt-undiv` `div-exp`
4×	`pow-prod-down` `associate-*l/`
3×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `div-inv` `associate-/l` `add-log-exp`
2×	`*-commutative` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-*r/` `clear-num`

Counts

3 → 104

Calls

3 calls:

13.0ms	(/ (sin (* 0.5 x)) (sin x))
61.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
32.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series182.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (sin (* 0.5 x)) (sin x))
83.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* 0.5 x)) (sin x)))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify73.0ms

Counts

113 → 113

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	474	1006
1	2505	814
2	5001	799
done	5001	799

prune347.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) 3.0)
0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log` `add-cbrt-cube`
27×	`times-frac`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
10×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
3×	`expm1-log1p-u` `associate-*r/` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative`

Counts

3 → 99

Calls

3 calls:

12.0ms	(/ (sin (* 0.5 x)) 3.0)
17.0ms	(/ (sin (* 0.5 x)) (sin x))
37.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

series181.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(/ (sin (* 0.5 x)) 3.0)
43.0ms	(/ (sin (* 0.5 x)) (sin x))
90.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin (* 0.5 x)) (sin x)))

simplify67.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	437	968
1	2144	808
2	5001	786
done	5001	786

prune310.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* 0.5 x)) (sin x))
0.2b	(/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0)))
0.2b	(* (* 8.0 (/ (/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
0.4b	(/ (/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

rewrite170.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
65×	`add-exp-log`
51×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
48×	`add-cbrt-cube`
24×	`cbrt-prod`
23×	`cbrt-undiv` `div-exp`
22×	`prod-exp` `cbrt-unprod`
13×	`associate-r` `associate-/l*`
11×	`div-inv`
10×	`associate-/r*`
9×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
1×	`frac-times` `associate-l` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 175

Calls

4 calls:

13.0ms	(/ (sin (* 0.5 x)) (sin x))
18.0ms	(/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0)))
105.0ms	(* (* 8.0 (/ (/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
28.0ms	(/ (/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

series524.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (sin (* 0.5 x)) (sin x))
134.0ms	(/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0)))
197.0ms	(* (* 8.0 (/ (/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))) (/ (sin (* 0.5 x)) (sin x)))
137.0ms	(/ (/ (sin (* 0.5 x)) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

simplify105.0ms

Counts

187 → 187

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	753	2381
1	3687	1920
2	5002	1799
done	5002	1799

prune843.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes44.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	14
1	17	14
done	17	14

end0.0ms

sample1.8s

Algorithm

intervals

Results

785.0ms	1554×	body	1280	valid
424.0ms	1284×	body	640	valid
271.0ms	4267×	body	80	valid
132.0ms	623×	body	320	valid
40.0ms	272×	body	160	valid