Details

sample165.0ms

Algorithm

intervals

Results

62.0ms	51×	body	1280	valid
51.0ms	147×	body	80	valid
29.0ms	34×	body	640	valid
7.0ms	11×	body	320	valid
5.0ms	13×	body	160	valid

simplify250.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	275
7	275
6	274
5	226
4	134
3	71
2	35
1	20
0	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
18.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
19×	`add-sqr-sqrt`
14×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
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×	`associate-/r*` `insert-posit16` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 82

Calls

3 calls:

66.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
20.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
66.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series204.0ms

Counts

3 → 9

Calls

3 calls:

62.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
46.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
96.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.6s

Counts

91 → 91

Iterations

Iter	Nodes
done	5003
2	1441
1	414
0	166

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.1b	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
0.2b	(/ (sin x) (sin (* x 0.5)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

153×	`times-frac`
98×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
44×	`associate-l`
19×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
10×	`div-inv`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*`
5×	`pow1`
3×	`associate-r` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`pow-prod-down` `associate-l/` `-commutative`

Counts

3 → 166

Calls

3 calls:

18.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
26.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
14.0ms	(/ (sin x) (sin (* x 0.5)))

series178.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
75.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) 2.6666666666666665)
46.0ms	(/ (sin x) (sin (* x 0.5)))

simplify1.6s

Counts

175 → 175

Iterations

Iter	Nodes
done	5002
2	2455
1	677
0	255

prune729.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
0.3b	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
111×	`add-sqr-sqrt`
93×	`*-un-lft-identity` `add-cube-cbrt`
45×	`associate-l`
34×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
12×	`associate-r`
11×	`pow1`
10×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
9×	`sqrt-prod`
6×	`associate-/l*` `unswap-sqr`
4×	`pow-prod-down` `insert-posit16` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `associate-/r/` `*-commutative`

Counts

4 → 199

Calls

4 calls:

18.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
11.0ms	(/ (sin x) (sin (* x 0.5)))
62.0ms	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
32.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))

series401.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
57.0ms	(/ (sin x) (sin (* x 0.5)))
154.0ms	(* (* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
111.0ms	(* (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5)))) (sqrt 2.6666666666666665))

simplify2.1s

Counts

211 → 211

Iterations

Iter	Nodes
done	5000
2	2996
1	811
0	297

prune937.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))
0.3b	(* (* (* 1 (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
0.3b	(* (* 1 (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
66×	`add-exp-log`
58×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
45×	`add-cbrt-cube`
34×	`prod-exp`
19×	`cbrt-unprod`
18×	`pow1`
16×	`associate-/r*` `div-exp`
12×	`associate-r`
10×	`cbrt-undiv`
9×	`pow-prod-down`
6×	`1-exp` `sqrt-prod` `div-inv` `associate-/l*`
4×	`insert-posit16` `add-log-exp`
3×	`associate-*l/`
2×	`clear-num` `frac-2neg` `associate-l` `associate-r/` `-commutative`
1×	`associate-/r/`

Counts

4 → 162

Calls

4 calls:

26.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
16.0ms	(/ (sin x) (sin (* x 0.5)))
201.0ms	(* (* (* 1 (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
54.0ms	(* (* 1 (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665))

series482.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))
63.0ms	(/ (sin x) (sin (* x 0.5)))
200.0ms	(* (* (* 1 (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665)) (sqrt 2.6666666666666665))
138.0ms	(* (* 1 (/ (sin (* x 0.5)) (/ (sin x) (sin (* x 0.5))))) (sqrt 2.6666666666666665))

simplify2.2s

Counts

174 → 174

Iterations

Iter	Nodes
done	5000
2	2397
1	732
0	285

prune644.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes90.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
1	19
0	13

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.4s	1532×	body	1280	valid
1.8s	1302×	body	640	valid
877.0ms	4274×	body	80	valid
442.0ms	578×	body	320	valid
121.0ms	314×	body	160	valid