Details

sample76.0ms

Algorithm

intervals

Results

28.0ms	44×	body	1280	valid
18.0ms	43×	body	640	valid
11.0ms	140×	body	80	valid
5.0ms	17×	body	320	valid
2.0ms	12×	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

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: 17.5b

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)))
17.3b	(/ (* (* (/ 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)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series25.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
4.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
12.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (46.0ms)

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

prune196.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

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:

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

series22.0ms

Counts

3 → 9

Calls

3 calls:

12.0ms	(/ (* (/ 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)))

simplify64.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (53.0ms)

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

prune251.0ms

Filtered

90 candidates to 119 candidates (-32.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	120	11	131

Merged error: 0b

Counts

131 → 11

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

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:

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

series28.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
7.0ms	(/ (sin x) (sin (* 0.5 x)))
12.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	423	884
1	2225	705
2	5001	686

prune175.0ms

Filtered

65 candidates to 94 candidates (-44.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 0b

Counts

105 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(* (/ (sqrt 8.0) (sqrt 3.0)) (* (/ (sqrt 8.0) (sqrt 3.0)) (sin (* x 0.5))))
1.0b	(/ (sqrt 8.0) (sqrt 3.0))
1.0b	(/ (sqrt 8.0) (sqrt 3.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

120×	`sqrt-prod`
117×	`times-frac`
93×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
40×	`associate-l`
31×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r` `associate-/l`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1`
8×	`cbrt-undiv` `div-exp`
4×	`div-inv` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `associate-*l/` `clear-num`
2×	`sqrt-undiv`
1×	`frac-times` `associate-r/` `associate-r` `-commutative`

Counts

4 → 215

Calls

4 calls:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
17.0ms	(* (/ (sqrt 8.0) (sqrt 3.0)) (* (/ (sqrt 8.0) (sqrt 3.0)) (sin (* x 0.5))))
5.0ms	(/ (sqrt 8.0) (sqrt 3.0))
5.0ms	(/ (sqrt 8.0) (sqrt 3.0))

series26.0ms

Counts

4 → 8

Calls

4 calls:

7.0ms	(/ (sin x) (sin (* 0.5 x)))
19.0ms	(* (/ (sqrt 8.0) (sqrt 3.0)) (* (/ (sqrt 8.0) (sqrt 3.0)) (sin (* x 0.5))))
0.0ms	(/ (sqrt 8.0) (sqrt 3.0))
0.0ms	(/ (sqrt 8.0) (sqrt 3.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

223 → 223

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	515	2005
1	2303	1729
2	5002	1616

prune491.0ms

Filtered

131 candidates to 223 candidates (-70.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	223	0	223
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	223	11	234

Merged error: 0b

Counts

234 → 11

regimes62.0ms

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	15	9
1	17	9
2	17	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

989.0ms	1536×	body	1280	valid
517.0ms	1262×	body	640	valid
370.0ms	4305×	body	80	valid
156.0ms	573×	body	320	valid
62.0ms	324×	body	160	valid

Details

sample76.0ms

simplify15.0ms

prune3.0ms

localize10.0ms

rewrite27.0ms

series25.0ms

simplify54.0ms

prune196.0ms

localize13.0ms

rewrite26.0ms

series22.0ms

simplify64.0ms

prune251.0ms

localize13.0ms

rewrite24.0ms

series28.0ms

simplify53.0ms

prune175.0ms

localize17.0ms

rewrite42.0ms

series26.0ms

simplify65.0ms

prune491.0ms

regimes62.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

Profiling