Details

sample71.0ms

Algorithm

intervals

Results

28.0ms	52×	body	1280	valid
13.0ms	35×	body	640	valid
10.0ms	132×	body	80	valid
7.0ms	25×	body	320	valid
2.0ms	12×	body	160	valid

simplify264.0ms

Counts

1 → 1

Iterations

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize27.0ms

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)))
14.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite151.0ms

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*` `add-log-exp`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `associate-/l*` `associate-/l/`

Counts

3 → 79

Calls

3 calls:

60.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
20.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
68.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series237.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
53.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
109.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1399
1	411
0	163

prune391.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`*-un-lft-identity` `add-cube-cbrt`
31×	`add-cbrt-cube` `add-exp-log`
16×	`associate-/r*`
13×	`cbrt-undiv` `div-exp` `associate-l`
6×	`prod-exp` `cbrt-unprod`
5×	`pow1` `div-inv`
4×	`associate-/l*`
3×	`associate-r` `add-log-exp`
2×	`clear-num` `frac-2neg` `associate-*l/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 110

Calls

3 calls:

39.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
14.0ms	(/ (sin x) (sin (* x 0.5)))
35.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series200.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
55.0ms	(/ (sin x) (sin (* x 0.5)))
42.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.6s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	2046
1	549
0	211

prune670.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite149.0ms

Algorithm

rewrite-expression-head

Rules

1985×	`times-frac`
858×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
108×	`div-inv`
50×	`associate-/l*`
31×	`add-cbrt-cube` `add-exp-log`
29×	`associate-/r*`
19×	`cbrt-undiv` `div-exp`
16×	`associate-/r/`
3×	`pow1` `clear-num` `frac-2neg` `add-log-exp`
1×	`associate-/l/`

Counts

3 → 750

Calls

3 calls:

12.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
39.0ms	(/ (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin x) (sin (* x 0.5))))
9.0ms	(/ (sin x) (sin (* x 0.5)))

series236.0ms

Counts

3 → 9

Calls

3 calls:

47.0ms	(/ (sin (* x 0.5)) (/ 3.0 8.0))
116.0ms	(/ (/ (sin (* x 0.5)) (/ 3.0 8.0)) (/ (sin x) (sin (* x 0.5))))
72.0ms	(/ (sin x) (sin (* x 0.5)))

simplify2.3s

Counts

759 → 759

Iterations

Iter	Nodes
done	5000
1	4647
0	1342

prune5.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

60×	`add-sqr-sqrt`
58×	`times-frac`
48×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
7×	`cbrt-div`
6×	`frac-times` `cbrt-undiv` `associate-/r` `div-exp` `associate-l/` `div-inv` `associate-/l*`
4×	`prod-exp` `associate-*r/` `cbrt-unprod` `add-log-exp` `unswap-sqr`
2×	`clear-num` `frac-2neg`
1×	`cbrt-prod` `pow2` `pow-plus` `pow1/3` `pow3` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `rem-cbrt-cube`

Counts

4 → 138

Calls

4 calls:

9.0ms	(/ (sin x) (sin (* x 0.5)))
11.0ms	(/ (sin x) (sin (* x 0.5)))
35.0ms	(* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
50.0ms	(cbrt (* (* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5)))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(/ (sin x) (sin (* x 0.5)))
48.0ms	(/ (sin x) (sin (* x 0.5)))
84.0ms	(* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
45.0ms	(cbrt (* (* (/ (sin x) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5)))) (/ (sin x) (sin (* x 0.5)))))

simplify3.2s

Counts

150 → 150

Iterations

Iter	Nodes
done	5000
3	4621
2	1713
1	489
0	163

prune783.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes58.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	22
1	22
0	17

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.4s	1208×	body	640	valid
1.3s	1552×	body	1280	valid
529.0ms	637×	body	320	valid
516.0ms	4287×	body	80	valid
72.0ms	316×	body	160	valid