Details

sample80.0ms

Algorithm

intervals

Results

33.0ms	50×	body	1280	valid
16.0ms	38×	body	640	valid
13.0ms	133×	body	80	valid
6.0ms	21×	body	320	valid
3.0ms	14×	body	160	valid

simplify100.0ms

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	244	16
6	262	16
done	262	16

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 12.9b

Counts

2 → 1

localize11.0ms

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)))
12.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite32.0ms

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:

10.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series26.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
4.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
15.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify442.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	163	1474
1	413	1285
2	1685	1016
done	5000	1016

prune195.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 0.0b

Counts

89 → 10

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

rewrite29.0ms

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:

5.0ms	(/ (sin (* x 0.5)) (sin x))
12.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
8.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series27.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/ (sin (* x 0.5)) (sin x))
13.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify494.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (148.0ms)

Iter	Nodes	Cost
0	183	1718
1	462	1555
2	1905	1292
done	5000	1292

prune223.0ms

Filtered

80 candidates to 107 candidates (-33.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	108	9	117

Merged error: 0b

Counts

117 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
37×	`times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
26×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`cbrt-undiv` `div-exp`
6×	`associate-/r` `associate-/l`
4×	`associate-r/` `associate-l*` `pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `unswap-sqr`
1×	`frac-times` `associate-*l/`

Counts

4 → 125

Calls

4 calls:

8.0ms	(* 8.0 (/ (sin (* x 0.5)) 3.0))
5.0ms	(/ (sin (* x 0.5)) 3.0)
5.0ms	(/ (sin (* x 0.5)) (sin x))
11.0ms	(* (* 8.0 (/ (sin (* x 0.5)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

series27.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 8.0 (/ (sin (* x 0.5)) 3.0))
4.0ms	(/ (sin (* x 0.5)) 3.0)
7.0ms	(/ (sin (* x 0.5)) (sin x))
12.0ms	(* (* 8.0 (/ (sin (* x 0.5)) 3.0)) (/ (sin (* x 0.5)) (sin x)))

simplify494.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (156.0ms)

Iter	Nodes	Cost
0	206	2070
1	513	1976
2	2059	1601
done	5000	1601

prune270.0ms

Filtered

102 candidates to 137 candidates (-34.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	137	9	146

Merged error: 0b

Counts

146 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
0.2b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
0.5b	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
1.0b	(/ 8.0 (cbrt 3.0))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

313×	`add-exp-log`
178×	`prod-exp`
122×	`add-cbrt-cube`
81×	`div-exp`
76×	`cbrt-unprod`
50×	`add-sqr-sqrt` `times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
39×	`cbrt-undiv`
30×	`associate-l`
22×	`cbrt-prod`
20×	`pow1`
18×	`rec-exp` `1-exp`
17×	`associate-r`
13×	`associate-*l/`
10×	`pow-prod-down`
6×	`frac-times` `associate-/r*`
4×	`associate-*r/` `div-inv` `add-log-exp`
3×	`-commutative` `associate-/l` `unswap-sqr`
1×	`frac-2neg` `clear-num`

Counts

4 → 228

Calls

4 calls:

23.0ms	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
17.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
10.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
4.0ms	(/ 8.0 (cbrt 3.0))

series53.0ms

Counts

4 → 10

Calls

4 calls:

22.0ms	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
16.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
14.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify897.0ms

Counts

238 → 238

Iterations

Useful iterations: 2 (328.0ms)

Iter	Nodes	Cost
0	341	5792
1	1041	5101
2	4301	3309
done	5000	3309

prune440.0ms

Filtered

126 candidates to 238 candidates (-88.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	239	8	247

Merged error: 0b

Counts

247 → 8

regimes51.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	14	16
done	14	16

end0.0ms

sample2.4s

Algorithm

intervals

Results

994.0ms	1510×	body	1280	valid
524.0ms	1208×	body	640	valid
461.0ms	4389×	body	80	valid
187.0ms	608×	body	320	valid
67.0ms	285×	body	160	valid

Details

sample80.0ms

simplify100.0ms

prune3.0ms

localize11.0ms

rewrite32.0ms

series26.0ms

simplify442.0ms

prune195.0ms

localize11.0ms

rewrite29.0ms

series27.0ms

simplify494.0ms

prune223.0ms

localize13.0ms

rewrite33.0ms

series27.0ms

simplify494.0ms

prune270.0ms

localize17.0ms

rewrite69.0ms

series53.0ms

simplify897.0ms

prune440.0ms

regimes51.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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