Details

sample82.0ms

Algorithm

intervals

Results

32.0ms	50×	body	1280	valid
17.0ms	38×	body	640	valid
14.0ms	133×	body	80	valid
6.0ms	21×	body	320	valid
3.0ms	14×	body	160	valid

simplify204.0ms

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

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

localize10.0ms

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))

rewrite35.0ms

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:

9.0ms	(* (* (/ 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))

series23.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify829.0ms

Counts

88 → 88

Iterations

Useful iterations: 2 (234.0ms)

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

prune196.0ms

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

localize13.0ms

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)))

rewrite28.0ms

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))
11.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin (* x 0.5)) (sin x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series24.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify965.0ms

Counts

107 → 107

Iterations

Useful iterations: 2 (382.0ms)

Iter	Nodes	Cost
0	183	1718
1	453	1555
2	1768	1292
done	5000	1292

prune211.0ms

Filtered

78 candidates to 107 candidates (-37.2%)

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

localize11.0ms

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)))

rewrite35.0ms

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))
13.0ms	(* (* 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)))

simplify810.0ms

Counts

137 → 137

Iterations

Useful iterations: 2 (295.0ms)

Iter	Nodes	Cost
0	206	2070
1	502	1976
2	1785	1605
done	5001	1605

prune265.0ms

Filtered

101 candidates to 137 candidates (-35.6%)

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

localize18.0ms

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))

rewrite68.0ms

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))

series58.0ms

Counts

4 → 10

Calls

4 calls:

27.0ms	(* (* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))) (/ (sin (* x 0.5)) (sin x)))
20.0ms	(* (/ 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)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify1.4s

Counts

238 → 238

Iterations

Useful iterations: 2 (623.0ms)

Iter	Nodes	Cost
0	341	5792
1	1025	5089
2	3534	3343
done	5000	3343

prune423.0ms

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

regimes49.0ms

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

981.0ms	1510×	body	1280	valid
516.0ms	1208×	body	640	valid
465.0ms	4389×	body	80	valid
178.0ms	608×	body	320	valid
59.0ms	285×	body	160	valid

Details

sample82.0ms

simplify204.0ms

prune3.0ms

localize10.0ms

rewrite35.0ms

series23.0ms

simplify829.0ms

prune196.0ms

localize13.0ms

rewrite28.0ms

series24.0ms

simplify965.0ms

prune211.0ms

localize11.0ms

rewrite35.0ms

series27.0ms

simplify810.0ms

prune265.0ms

localize18.0ms

rewrite68.0ms

series58.0ms

simplify1.4s

prune423.0ms

regimes49.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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