Details

sample85.0ms

Algorithm

intervals

Results

30.0ms	46×	body	1280	valid
19.0ms	140×	body	80	valid
15.0ms	34×	body	640	valid
7.0ms	21×	body	320	valid
3.0ms	15×	body	160	valid

simplify321.0ms

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: 13.4b

localize17.0ms

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)))
13.2b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite223.0ms

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:

91.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
89.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series229.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
49.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
105.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: 2 (286.0ms)

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

prune228.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize11.0ms

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

rewrite109.0ms

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:

13.0ms	(/ (sin (* x 0.5)) (sin x))
63.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
28.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series199.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(/ (sin (* x 0.5)) (sin x))
102.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
39.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify2.0s

Counts

107 → 107

Iterations

Useful iterations: 2 (324.0ms)

Iter	Nodes	Cost
0	183	1718
1	436	1555
2	1584	1292
done	5000	1292

prune328.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite73.0ms

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:

20.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
12.0ms	(/ (sin (* x 0.5)) (sin x))
38.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
40.0ms	(/ (sin (* x 0.5)) (sin x))
78.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ (sin (* x 0.5)) (sin x)))

simplify1.4s

Counts

103 → 103

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	178	1743
1	440	1668
2	1620	1322
done	5001	1318

prune463.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

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:

33.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
29.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
108.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))
26.0ms	(/ (sin x) (sin (* x 0.5)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/ (* (sin (* 0.5 x)) 8.0) 3.0)
70.0ms	(/ 1 (/ (sin x) (sin (* x 0.5))))
124.0ms	(* (/ (* (sin (* 0.5 x)) 8.0) 3.0) (/ 1 (/ (sin x) (sin (* x 0.5)))))
69.0ms	(/ (sin x) (sin (* x 0.5)))

simplify1.4s

Counts

235 → 235

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	333	4532
1	843	3930
2	2524	3315
done	5001	3233

prune619.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes39.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	21
1	22	21
done	22	21

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	1542×	body	1280	valid
1.0s	1200×	body	640	valid
725.0ms	4318×	body	80	valid
294.0ms	644×	body	320	valid
115.0ms	296×	body	160	valid