Details

analyze975.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample74.0ms

Algorithm

intervals

Results

26.0ms	37×	body	1280	valid
19.0ms	47×	body	640	valid
14.0ms	143×	body	80	valid
6.0ms	22×	body	320	valid
1.0ms	7×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	43	9
2	93	9
3	174	9
4	269	9
5	288	9
6	288	9

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: 14.9b

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)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.8b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite27.0ms

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:

8.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
9.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series24.0ms

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)))
14.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify56.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	402	818
1	2097	614
2	5002	599

prune180.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	11	89

Merged error: 0.1b

Counts

89 → 11

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 110

Calls

3 calls:

9.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series21.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
6.0ms	(/ (sin x) (sin (* 0.5 x)))
4.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify69.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	540	1166
1	2701	980
2	5001	956

prune274.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	121	9	130

Merged error: 0.0b

Counts

130 → 9

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

49×	`times-frac`
33×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
28×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
13×	`cbrt-undiv` `div-exp`
7×	`associate-/l*`
5×	`div-inv`
4×	`prod-exp` `cbrt-unprod`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`
1×	`associate-*r/` `associate-/r/` `associate-/l/`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ (sin (* 0.5 x)) 3.0)
10.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
5.0ms	(/ (sin x) (sin (* 0.5 x)))

series24.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
13.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
8.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	504	1132
1	2553	976
2	5002	950

prune229.0ms

Filtered

84 candidates to 114 candidates (-35.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Merged error: 0.0b

Counts

123 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 2.6666666666666665 (sin (* 0.5 x)))
0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* 2.6666666666666665 (sin (* 0.5 x))) (/ (sin x) (sin (* 0.5 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`times-frac`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`div-inv` `associate-/l*`
3×	`associate-r` `associate-l` `prod-exp` `cbrt-unprod` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `unswap-sqr`

Counts

3 → 91

Calls

3 calls:

5.0ms	(* 2.6666666666666665 (sin (* 0.5 x)))
5.0ms	(/ (sin x) (sin (* 0.5 x)))
9.0ms	(/ (* 2.6666666666666665 (sin (* 0.5 x))) (/ (sin x) (sin (* 0.5 x))))

series25.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(* 2.6666666666666665 (sin (* 0.5 x)))
8.0ms	(/ (sin x) (sin (* 0.5 x)))
13.0ms	(/ (* 2.6666666666666665 (sin (* 0.5 x))) (/ (sin x) (sin (* 0.5 x))))

simplify57.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	383	905
1	1829	788
2	5001	776

prune174.0ms

Filtered

72 candidates to 100 candidates (-38.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	100	9	109

Merged error: 0.0b

Counts

109 → 9

regimes61.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

analyze884.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample2.6s

Algorithm

intervals

Results

1.1s	1538×	body	1280	valid
575.0ms	1222×	body	640	valid
465.0ms	4305×	body	80	valid
201.0ms	615×	body	320	valid
67.0ms	320×	body	160	valid

Details

analyze975.0ms

sample74.0ms

simplify14.0ms

prune3.0ms

localize10.0ms

rewrite27.0ms

series24.0ms

simplify56.0ms

prune180.0ms

localize13.0ms

rewrite27.0ms

series21.0ms

simplify69.0ms

prune274.0ms

localize11.0ms

rewrite25.0ms

series24.0ms

simplify69.0ms

prune229.0ms

localize10.0ms

rewrite22.0ms

series25.0ms

simplify57.0ms

prune174.0ms

regimes61.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze884.0ms

sample2.6s

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