Details

analyze782.0ms

Algorithm: search

sample75.0ms

Algorithm

intervals

Results

31.0ms	47×	body	1280	valid
18.0ms	43×	body	640	valid
13.0ms	145×	body	80	valid
5.0ms	17×	body	320	valid
1.0ms	4×	body	160	valid

simplify15.0ms

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

prune6.0ms

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: 15.5b

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)))
15.4b	(/ (* (* (/ 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)))
6.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series20.0ms

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

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

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

prune172.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	79	9	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 0.1b

Counts

89 → 9

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

rewrite23.0ms

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

series20.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(/ (* (/ 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)))

simplify66.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

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

prune219.0ms

Filtered

90 candidates to 119 candidates (-32.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	5	119
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	120	8	128

Merged error: 0b

Counts

128 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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:

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

series20.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	504	1132
1	2553	976
2	5001	950

prune244.0ms

Filtered

85 candidates to 114 candidates (-34.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	114	8	122

Merged error: 0b

Counts

122 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-exp-log`
49×	`add-cbrt-cube`
35×	`add-sqr-sqrt`
31×	`div-exp`
30×	`times-frac`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt`
26×	`prod-exp`
18×	`cbrt-undiv`
14×	`cbrt-unprod`
13×	`associate-r`
7×	`pow1` `associate-/r` `associate-/l`
5×	`rec-exp` `1-exp`
4×	`div-inv` `add-log-exp`
3×	`frac-2neg` `associate-r/` `associate-l*` `clear-num` `unswap-sqr`
2×	`associate-/r/` `un-div-inv`
1×	`pow-flip` `pow-prod-down` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 134

Calls

4 calls:

4.0ms	(/ 1 (sin (* 0.5 x)))
11.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (* (sin x) (/ 1 (sin (* 0.5 x)))))
4.0ms	(/ (sin (* 0.5 x)) 3.0)
7.0ms	(* (sin x) (/ 1 (sin (* 0.5 x))))

series28.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (sin (* 0.5 x)))
13.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (* (sin x) (/ 1 (sin (* 0.5 x)))))
3.0ms	(/ (sin (* 0.5 x)) 3.0)
6.0ms	(* (sin x) (/ 1 (sin (* 0.5 x))))

simplify69.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	582	1273
1	3058	1003
2	5002	944

prune176.0ms

Filtered

81 candidates to 146 candidates (-80.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	147	7	154

Merged error: 0b

Counts

154 → 7

regimes44.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	18	10

end0.0ms

analyze782.0ms

Algorithm: search

sample2.4s

Algorithm

intervals

Results

1.1s	1584×	body	1280	valid
542.0ms	1285×	body	640	valid
413.0ms	4211×	body	80	valid
172.0ms	607×	body	320	valid
65.0ms	313×	body	160	valid

Details

analyze782.0ms

sample75.0ms

simplify15.0ms

prune6.0ms

localize11.0ms

rewrite27.0ms

series20.0ms

simplify52.0ms

prune172.0ms

localize13.0ms

rewrite23.0ms

series20.0ms

simplify66.0ms

prune219.0ms

localize12.0ms

rewrite20.0ms

series20.0ms

simplify62.0ms

prune244.0ms

localize12.0ms

rewrite30.0ms

series28.0ms

simplify69.0ms

prune176.0ms

regimes44.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze782.0ms

sample2.4s

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