Details

sample322.0ms

Algorithm

intervals

Results

128.0ms	121×	body	80	valid
80.0ms	55×	body	640	valid
65.0ms	42×	body	1280	valid
14.0ms	27×	body	320	valid
8.0ms	11×	body	160	valid

simplify946.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	274
7	274
6	273
5	226
4	134
3	71
2	35
1	20
0	11

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize40.0ms

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)))
13.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite356.0ms

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:

150.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
58.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
133.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series412.0ms

Counts

3 → 9

Calls

3 calls:

125.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
78.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
208.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify3.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1423
1	418
0	169

prune848.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 97

Calls

3 calls:

38.0ms	(* (sin (* 0.5 x)) 2.6666666666666665)
55.0ms	(/ (* (sin (* 0.5 x)) 2.6666666666666665) (/ (sin x) (sin (* 0.5 x))))
24.0ms	(/ (sin x) (sin (* 0.5 x)))

series330.0ms

Counts

3 → 9

Calls

3 calls:

76.0ms	(* (sin (* 0.5 x)) 2.6666666666666665)
168.0ms	(/ (* (sin (* 0.5 x)) 2.6666666666666665) (/ (sin x) (sin (* 0.5 x))))
85.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify2.6s

Counts

106 → 106

Iterations

Iter	Nodes
done	5033
2	1754
1	431
0	172

prune970.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

477×	`times-frac`
237×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
49×	`associate-/r*`
23×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
10×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
1×	`associate-/r/` `associate-/l/`

Counts

3 → 295

Calls

3 calls:

46.0ms	(/ (/ (sin x) (sin (* 0.5 x))) 2.6666666666666665)
25.0ms	(/ (sin x) (sin (* 0.5 x)))
71.0ms	(/ (sin (* 0.5 x)) (/ (/ (sin x) (sin (* 0.5 x))) 2.6666666666666665))

series398.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(/ (/ (sin x) (sin (* 0.5 x))) 2.6666666666666665)
88.0ms	(/ (sin x) (sin (* 0.5 x)))
179.0ms	(/ (sin (* 0.5 x)) (/ (/ (sin x) (sin (* 0.5 x))) 2.6666666666666665))

simplify5.4s

Counts

304 → 304

Iterations

Iter	Nodes
done	5001
2	3893
1	1357
0	500

prune2.9s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sqrt 2.6666666666666665))
0.3b	(/ (sin (* 0.5 x)) (/ (sin x) (sqrt 2.6666666666666665)))
0.3b	(/ (/ (sin (* 0.5 x)) (/ (sin x) (sqrt 2.6666666666666665))) (/ (/ 1 (sin (* 0.5 x))) (sqrt 2.6666666666666665)))
0.4b	(/ (/ 1 (sin (* 0.5 x))) (sqrt 2.6666666666666665))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

25583×	`times-frac`
10285×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5139×	`sqrt-prod`
851×	`div-inv`
116×	`associate-/r*`
90×	`associate-/l*`
85×	`associate-/r/`
80×	`add-exp-log`
58×	`div-exp`
52×	`add-cbrt-cube`
34×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `rec-exp` `frac-2neg` `1-exp` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/l/`

Counts

4 → 6278

Calls

4 calls:

22.0ms	(/ (sin x) (sqrt 2.6666666666666665))
42.0ms	(/ (sin (* 0.5 x)) (/ (sin x) (sqrt 2.6666666666666665)))
359.0ms	(/ (/ (sin (* 0.5 x)) (/ (sin x) (sqrt 2.6666666666666665))) (/ (/ 1 (sin (* 0.5 x))) (sqrt 2.6666666666666665)))
43.0ms	(/ (/ 1 (sin (* 0.5 x))) (sqrt 2.6666666666666665))

series902.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (sin x) (sqrt 2.6666666666666665))
211.0ms	(/ (sin (* 0.5 x)) (/ (sin x) (sqrt 2.6666666666666665)))
330.0ms	(/ (/ (sin (* 0.5 x)) (/ (sin x) (sqrt 2.6666666666666665))) (/ (/ 1 (sin (* 0.5 x))) (sqrt 2.6666666666666665)))
229.0ms	(/ (/ 1 (sin (* 0.5 x))) (sqrt 2.6666666666666665))

simplify11.7s

Counts

6290 → 6290

Iterations

Iter	Nodes
done	6818
0	6818

prune1.0m

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

regimes133.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample6.7s

Algorithm

intervals

Results

2.3s	1507×	body	1280	valid
1.7s	1255×	body	640	valid
1.7s	4281×	body	80	valid
521.0ms	642×	body	320	valid
111.0ms	315×	body	160	valid