Details

sample52.0ms

Algorithm

intervals

Results

19.0ms	42×	body	1280	valid
10.0ms	33×	body	640	valid
10.0ms	150×	body	80	valid
4.0ms	18×	body	320	valid
2.0ms	13×	body	160	valid

simplify18.0ms

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: 16.8b

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)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
16.6b	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

rewrite28.0ms

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))

series174.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
41.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
80.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify63.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (49.0ms)

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

prune204.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	12	89

Merged error: 0.1b

Counts

89 → 12

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)))

rewrite25.0ms

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)))

series162.0ms

Counts

3 → 9

Calls

3 calls:

80.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
40.0ms	(/ (sin x) (sin (* 0.5 x)))
42.0ms	(* (/ 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	956

prune285.0ms

Filtered

119 candidates to 89 candidates (74.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	113	6	119
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	122	9	131

Merged error: 0b

Counts

131 → 9

localize10.0ms

Local error

Found 3 expressions with local error:

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)))

rewrite21.0ms

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:

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)))

series158.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(/ (sin (* 0.5 x)) 3.0)
77.0ms	(/ (* 8.0 (/ (sin (* 0.5 x)) 3.0)) (/ (sin x) (sin (* 0.5 x))))
39.0ms	(/ (sin x) (sin (* 0.5 x)))

simplify70.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (58.0ms)

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

prune227.0ms

Filtered

114 candidates to 84 candidates (73.7%)

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: 0b

Counts

123 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin (* x 0.5)))
0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
0.3b	(* (sin x) (/ 1 (sin (* x 0.5))))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

82×	`add-exp-log`
52×	`add-cbrt-cube`
40×	`add-sqr-sqrt`
31×	`times-frac` `div-exp`
29×	`*-un-lft-identity`
28×	`add-cube-cbrt` `prod-exp`
18×	`cbrt-undiv`
16×	`associate-r` `associate-l` `cbrt-unprod`
9×	`pow1`
5×	`rec-exp` `1-exp` `unswap-sqr`
4×	`associate-/r` `div-inv` `associate-/l` `add-log-exp`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `associate-/r/` `un-div-inv` `*-commutative`
1×	`pow-flip` `associate-/l/` `inv-pow`

Counts

4 → 139

Calls

4 calls:

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

series189.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ 1 (sin (* x 0.5)))
77.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (* (sin x) (/ 1 (sin (* x 0.5)))))
46.0ms	(* (sin x) (/ 1 (sin (* x 0.5))))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify78.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	604	1319
1	3198	988
2	5002	927

prune221.0ms

Filtered

151 candidates to 86 candidates (57.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	151	9	160

Merged error: 0b

Counts

160 → 9

regimes35.0ms

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	13	9
1	13	9

end0.0ms

sample1.7s

Algorithm

intervals

Results

691.0ms	1468×	body	1280	valid
383.0ms	1261×	body	640	valid
298.0ms	4314×	body	80	valid
136.0ms	637×	body	320	valid
45.0ms	320×	body	160	valid