Details

sample111.0ms

Algorithm

intervals

Results

35.0ms	47×	body	1280	valid
27.0ms	20×	body	320	valid
21.0ms	44×	body	640	valid
14.0ms	138×	body	80	valid
2.0ms	7×	body	160	valid

simplify354.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	43	16
3	93	16
4	173	16
5	277	16
6	314	16
done	314	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.0b

localize19.0ms

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))

rewrite242.0ms

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:

105.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
33.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
99.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series244.0ms

Counts

3 → 9

Calls

3 calls:

72.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
53.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
119.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify2.4s

Counts

88 → 88

Iterations

Useful iterations: 2 (390.0ms)

Iter	Nodes	Cost
0	163	1474
1	413	1285
2	2715	1064
done	5001	1064

prune301.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite166.0ms

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

Counts

3 → 98

Calls

3 calls:

17.0ms	(/ (sin (* x 0.5)) (sin x))
99.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
45.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series241.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(/ (sin (* x 0.5)) (sin x))
118.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
57.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.9s

Counts

107 → 107

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	183	1718
1	492	1676
2	3232	1342
done	5000	1292

prune376.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 94

Calls

3 calls:

22.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
21.0ms	(/ (sin (* x 0.5)) (sin x))
45.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin (* x 0.5)) (sin x)))

series237.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(/ (* 8.0 (sin (* 0.5 x))) 3.0)
62.0ms	(/ (sin (* x 0.5)) (sin x))
121.0ms	(* (/ (* 8.0 (sin (* 0.5 x))) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify2.2s

Counts

103 → 103

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	178	1755
1	489	1681
2	3546	1431
done	5001	1387

prune346.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
0.3b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

160×	`times-frac`
102×	`add-sqr-sqrt`
100×	`add-exp-log`
97×	`add-cube-cbrt` `*-un-lft-identity`
52×	`add-cbrt-cube`
47×	`associate-r`
37×	`div-exp` `prod-exp`
17×	`cbrt-undiv` `cbrt-unprod`
16×	`associate-/r*`
14×	`associate-l`
12×	`pow1`
11×	`div-inv`
8×	`rec-exp` `1-exp`
6×	`associate-/l*`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r/` `*-commutative` `unswap-sqr`
1×	`frac-times` `pow-flip` `associate-*r/` `un-div-inv` `inv-pow`

Counts

4 → 224

Calls

4 calls:

21.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
20.0ms	(/ (sin x) (sin (* 0.5 x)))
114.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
33.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
56.0ms	(/ (sin x) (sin (* 0.5 x)))
120.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
57.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify613.0ms

Counts

236 → 236

Iterations

Useful iterations: done (604.0ms)

Iter	Nodes	Cost
0	339	4363
1	1030	3867
done	5001	3380

prune710.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes45.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	13	16
1	15	16
2	16	16
done	16	16

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.3s	1481×	body	1280	valid
1.2s	1240×	body	640	valid
737.0ms	617×	body	320	valid
455.0ms	4347×	body	80	valid
117.0ms	315×	body	160	valid