Details

sample125.0ms

Algorithm

intervals

Results

49.0ms	46×	body	1280	valid
21.0ms	141×	body	80	valid
19.0ms	28×	body	640	valid
13.0ms	25×	body	320	valid
5.0ms	16×	body	160	valid

simplify398.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	89	16
4	168	16
5	257	16
6	273	16
done	273	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite249.0ms

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

Counts

3 → 79

Calls

3 calls:

108.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
99.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series241.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
52.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
110.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.2s

Counts

88 → 88

Iterations

Useful iterations: 2 (214.0ms)

Iter	Nodes	Cost
0	163	1474
1	395	1285
2	1428	1016
done	5000	1016

prune278.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

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

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
38×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
31×	`add-exp-log` `add-cbrt-cube`
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×	`frac-2neg` `associate-*l/` `clear-num` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

3 → 110

Calls

3 calls:

53.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
17.0ms	(/ (sin x) (sin (* x 0.5)))
33.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series192.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* x 0.5))))
56.0ms	(/ (sin x) (sin (* x 0.5)))
48.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify1.4s

Counts

119 → 119

Iterations

Useful iterations: 2 (330.0ms)

Iter	Nodes	Cost
0	211	2048
1	502	1898
2	1807	1604
done	5000	1604

prune412.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 8.0 (sin (* 0.5 x)))
0.1b	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
0.1b	(/ (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin x) (sin (* x 0.5))))
0.2b	(/ (sin x) (sin (* x 0.5)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

217×	`times-frac`
102×	`add-sqr-sqrt`
100×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
25×	`div-inv`
19×	`associate-/r*`
16×	`cbrt-undiv` `div-exp`
11×	`associate-/l*`
6×	`pow1`
4×	`prod-exp` `cbrt-unprod` `add-log-exp`
3×	`frac-2neg` `associate-r` `associate-l` `clear-num`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 201

Calls

4 calls:

16.0ms	(* 8.0 (sin (* 0.5 x)))
34.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
37.0ms	(/ (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin x) (sin (* x 0.5))))
19.0ms	(/ (sin x) (sin (* x 0.5)))

series203.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 8.0 (sin (* 0.5 x)))
42.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
76.0ms	(/ (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin x) (sin (* x 0.5))))
49.0ms	(/ (sin x) (sin (* x 0.5)))

simplify1.4s

Counts

213 → 213

Iterations

Useful iterations: 2 (528.0ms)

Iter	Nodes	Cost
0	370	4906
1	992	4690
2	3391	4243
done	5000	4243

prune876.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sin x) (sin (* x 0.5))))
0.1b	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
0.2b	(/ (sin x) (sin (* x 0.5)))
0.2b	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
107×	`add-sqr-sqrt`
100×	`add-exp-log`
95×	`*-un-lft-identity`
93×	`add-cube-cbrt`
52×	`add-cbrt-cube`
45×	`div-exp`
44×	`associate-r`
29×	`prod-exp`
21×	`cbrt-undiv`
19×	`associate-/r*`
13×	`cbrt-unprod`
12×	`div-inv`
8×	`rec-exp` `1-exp`
7×	`pow1` `associate-l` `associate-/l*`
5×	`unswap-sqr`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `un-div-inv` `*-commutative` `inv-pow`

Counts

4 → 223

Calls

4 calls:

21.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
26.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
20.0ms	(/ (sin x) (sin (* x 0.5)))
89.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))

series272.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
50.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
64.0ms	(/ (sin x) (sin (* x 0.5)))
107.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))

simplify1.4s

Counts

235 → 235

Iterations

Useful iterations: 2 (523.0ms)

Iter	Nodes	Cost
0	333	4544
1	843	3942
2	2449	3236
done	5000	3236

prune628.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes32.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	20
1	21	20
done	21	20

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.5s	1546×	body	1280	valid
1.4s	1256×	body	640	valid
529.0ms	4253×	body	80	valid
310.0ms	634×	body	320	valid
75.0ms	311×	body	160	valid