Details

sample53.0ms

Algorithm

intervals

Results

15.0ms	35×	body	1280	valid
11.0ms	41×	body	640	valid
8.0ms	144×	body	80	valid
7.0ms	18×	body	320	valid
3.0ms	18×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 14.5b

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)))
14.3b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite29.0ms

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

series175.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
80.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (49.0ms)

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

prune231.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	74	14	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	14	89

Merged error: 0.1b

Counts

89 → 14

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* (/ 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)))

rewrite26.0ms

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:

10.0ms	(/ (* (/ 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)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
39.0ms	(/ (sin x) (sin (* 0.5 x)))
40.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify70.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	540	1166
1	2701	980
2	5001	963

prune298.0ms

Filtered

119 candidates to 88 candidates (73.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	7	6	13
Picked	1	0	1
Done	0	0	0
Total	121	12	133

Merged error: 0b

Counts

133 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

59×	`times-frac`
47×	`add-sqr-sqrt`
42×	`add-cube-cbrt` `*-un-lft-identity`
34×	`add-exp-log` `add-cbrt-cube`
19×	`associate-/r*`
14×	`cbrt-undiv` `div-exp`
13×	`associate-r`
7×	`associate-/l*`
6×	`pow1` `prod-exp` `cbrt-unprod` `div-inv`
4×	`add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num`
2×	`associate-*r/` `unswap-sqr`
1×	`pow-prod-down` `associate-/r/` `*-commutative` `associate-/l/`

Counts

4 → 137

Calls

4 calls:

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

series376.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* 8.0 (/ (sin (* 0.5 x)) 3.0))
221.0ms	(/ (sin (* 0.5 x)) 3.0)
79.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify78.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	579	1350
1	2925	1169
2	5001	1146

prune328.0ms

Filtered

149 candidates to 109 candidates (73.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	150	11	161

Merged error: 0b

Counts

161 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

159×	`times-frac`
97×	`add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
49×	`add-cbrt-cube`
44×	`associate-r`
37×	`div-exp`
35×	`prod-exp`
19×	`associate-/r*`
17×	`cbrt-undiv`
15×	`cbrt-unprod`
11×	`div-inv`
10×	`pow1`
9×	`associate-/l*`
8×	`rec-exp` `1-exp`
4×	`add-log-exp`
3×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num`
2×	`associate-/r/`
1×	`frac-times` `pow-flip` `associate-l` `associate-l/` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 219

Calls

4 calls:

4.0ms	(/ (sin (* 0.5 x)) 3.0)
6.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
16.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
4.0ms	(/ (sin x) (sin (* 0.5 x)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ (sin (* 0.5 x)) 3.0)
36.0ms	(/ 1 (/ (sin x) (sin (* 0.5 x))))
75.0ms	(* (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ 1 (/ (sin x) (sin (* 0.5 x)))))
43.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

231 → 231

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	902	2417
1	5001	2080

prune469.0ms

Filtered

231 candidates to 146 candidates (63.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	229	2	231
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	231	11	242

Merged error: 0b

Counts

242 → 11

regimes82.0ms

Accuracy

0% (0.3b 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	18	10
1	18	10

end0.0ms

sample1.6s

Algorithm

intervals

Results

678.0ms	1519×	body	1280	valid
357.0ms	1243×	body	640	valid
265.0ms	4304×	body	80	valid
122.0ms	628×	body	320	valid
42.0ms	306×	body	160	valid