Details

analyze2.8s

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 50.15564%

sample80.0ms

Algorithm

intervals

Results

38.0ms	57×	body	1280	valid
13.0ms	140×	body	80	valid
13.0ms	32×	body	640	valid
5.0ms	16×	body	320	valid
2.0ms	11×	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: 14.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
0.4b	(* (/ 8.0 3.0) (sin (* x 0.5)))
14.2b	(/ (* (* (/ 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:

9.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series21.0ms

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

prune178.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

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: 0.1b

Counts

89 → 10

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)))

rewrite24.0ms

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)))

series22.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

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

prune236.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	7	119
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 0b

Counts

129 → 10

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 85

Calls

3 calls:

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

series27.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	423	884
1	2206	701
2	5001	685

prune164.0ms

Filtered

65 candidates to 94 candidates (-44.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 0b

Counts

104 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.3b	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
0.4b	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
1.0b	(/ 8.0 (cbrt 3.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

91×	`add-exp-log`
51×	`add-sqr-sqrt`
50×	`times-frac`
46×	`prod-exp`
43×	`add-cube-cbrt` `*-un-lft-identity`
38×	`add-cbrt-cube`
29×	`associate-l`
22×	`cbrt-prod` `div-exp`
20×	`cbrt-unprod`
12×	`cbrt-undiv`
11×	`pow1`
9×	`associate-/r*`
6×	`rec-exp` `1-exp` `associate-/l*`
4×	`associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-*r/`

Counts

4 → 159

Calls

4 calls:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
15.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
8.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
4.0ms	(/ 8.0 (cbrt 3.0))

series31.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(/ (sin x) (sin (* 0.5 x)))
15.0ms	(* (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5))))
9.0ms	(* (/ 8.0 (cbrt 3.0)) (sin (* x 0.5)))
0.0ms	(/ 8.0 (cbrt 3.0))

simplify80.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	645	1472
1	2861	1212
2	5001	1122

prune369.0ms

Filtered

110 candidates to 169 candidates (-53.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	169	10	179

Merged error: 0b

Counts

179 → 10

regimes59.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	9
1	17	9
2	17	9

end0.0ms

analyze2.8s

Algorithm

sampling

Space saved by range analysis: 0.048828%

Space saved by search: 0.048828%

Guaranteed chance to sample good point: 50.15564%

sample2.6s

Algorithm

intervals

Results

1.0s	1515×	body	1280	valid
654.0ms	4312×	body	80	valid
552.0ms	1259×	body	640	valid
174.0ms	603×	body	320	valid
61.0ms	311×	body	160	valid

Details

analyze2.8s

sample80.0ms

simplify15.0ms

prune6.0ms

localize11.0ms

rewrite28.0ms

series21.0ms

simplify52.0ms

prune178.0ms

localize13.0ms

rewrite24.0ms

series22.0ms

simplify62.0ms

prune236.0ms

localize13.0ms

rewrite22.0ms

series27.0ms

simplify52.0ms

prune164.0ms

localize21.0ms

rewrite38.0ms

series31.0ms

simplify80.0ms

prune369.0ms

regimes59.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze2.8s

sample2.6s

Profiling