Details

sample60.0ms

Algorithm

intervals

Results

24.0ms	50×	body	1280	valid
11.0ms	37×	body	640	valid
8.0ms	128×	body	80	valid
4.0ms	20×	body	320	valid
3.0ms	21×	body	160	valid

simplify186.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	16
1	20	16
2	42	16
3	90	16
4	168	16
5	237	16
6	255	16
done	255	16

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.7b

localize13.0ms

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

rewrite55.0ms

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:

20.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
12.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
20.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series172.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
79.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify774.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (219.0ms)

Iter	Nodes	Cost
0	163	1474
1	403	1285
2	1604	1016
done	5000	1016

prune222.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin (* x 0.5)) (sin x))
0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite39.0ms

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:

4.0ms	(/ (sin (* x 0.5)) (sin x))
21.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
10.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ (sin (* x 0.5)) (sin x))
78.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify899.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (355.0ms)

Iter	Nodes	Cost
0	183	1718
1	453	1555
2	1768	1292
done	5001	1292

prune262.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
36×	`add-sqr-sqrt`
27×	`times-frac`
23×	`add-cube-cbrt` `*-un-lft-identity`
15×	`add-cbrt-cube`
13×	`associate-r` `prod-exp`
12×	`div-exp`
11×	`associate-l`
9×	`unpow-prod-down`
6×	`pow-exp` `associate-/r*` `unswap-sqr`
4×	`pow1` `cbrt-undiv` `div-inv` `associate-/l*`
3×	`cbrt-unprod` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `clear-num`
1×	`associate-r/` `pow-prod-down` `-commutative`

Counts

3 → 100

Calls

3 calls:

5.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
4.0ms	(/ (sin (* x 0.5)) (sin x))
19.0ms	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

series153.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ (* 8.0 (sin (* x 0.5))) 3.0)
38.0ms	(/ (sin (* x 0.5)) (sin x))
77.0ms	(* (pow (/ (* 8.0 (sin (* x 0.5))) 3.0) 1) (/ (sin (* x 0.5)) (sin x)))

simplify782.0ms

Counts

109 → 109

Iterations

Useful iterations: 2 (258.0ms)

Iter	Nodes	Cost
0	195	1946
1	461	1729
2	1683	1510
done	5000	1510

prune297.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

101×	`times-frac`
100×	`add-exp-log`
83×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
40×	`unpow-prod-down` `div-exp`
38×	`associate-l`
35×	`cbrt-prod`
32×	`prod-exp`
28×	`add-cbrt-cube`
18×	`div-inv`
15×	`cbrt-undiv`
13×	`associate-r`
12×	`pow-exp`
10×	`associate-/r*` `cbrt-unprod` `unswap-sqr`
9×	`associate-/l*`
5×	`pow1`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `sqr-pow`
2×	`pow-to-exp`
1×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`

Counts

4 → 199

Calls

4 calls:

7.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt 3.0) (cbrt 3.0)))
4.0ms	(/ (sin (* x 0.5)) (sin x))
49.0ms	(* (pow (/ (/ (* 8.0 (sin (* x 0.5))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1) (/ (sin (* x 0.5)) (sin x)))
9.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

series509.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (cbrt 3.0) (cbrt 3.0)))
38.0ms	(/ (sin (* x 0.5)) (sin x))
171.0ms	(* (pow (/ (/ (* 8.0 (sin (* x 0.5))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0)) 1) (/ (sin (* x 0.5)) (sin x)))
138.0ms	(/ (/ (* 8.0 (sin (* x 0.5))) (* (cbrt 3.0) (cbrt 3.0))) (cbrt 3.0))

simplify1.3s

Counts

211 → 211

Iterations

Useful iterations: 2 (642.0ms)

Iter	Nodes	Cost
0	338	5131
1	862	4227
2	3419	3543
done	5000	3543

prune673.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0b

regimes42.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: done (1.0ms)

Iter	Nodes	Cost
0	13	18
1	18	18
done	18	16

end0.0ms

sample1.7s

Algorithm

intervals

Results

726.0ms	1449×	body	1280	valid
409.0ms	1309×	body	640	valid
272.0ms	4315×	body	80	valid
127.0ms	599×	body	320	valid
47.0ms	328×	body	160	valid