Details

sample60.0ms

Algorithm

intervals

Results

25.0ms	50×	body	1280	valid
11.0ms	38×	body	640	valid
8.0ms	133×	body	80	valid
5.0ms	25×	body	320	valid
1.0ms	10×	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: 13.5b

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)))
13.3b	(/ (* (* (/ 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)))
10.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

series166.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5)))
37.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))
76.0ms	(/ (* (* (/ 8.0 3.0) (sin (* x 0.5))) (sin (* x 0.5))) (sin x))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (48.0ms)

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

prune228.0ms

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

localize14.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin x) (sin (* 0.5 x)))
0.2b	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
0.3b	(* (/ 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:

4.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ (sin x) (sin (* 0.5 x))))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify67.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (54.0ms)

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

prune341.0ms

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

localize15.0ms

Local error

Found 3 expressions with local error:

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

7.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
4.0ms	(/ (sin x) (sin (* 0.5 x)))
10.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

series178.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(* (/ (sin x) (sin (* 0.5 x))) 3.0)
39.0ms	(/ (sin x) (sin (* 0.5 x)))
77.0ms	(/ (* 8.0 (sin (* x 0.5))) (* (/ (sin x) (sin (* 0.5 x))) 3.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (47.0ms)

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

prune244.0ms

Filtered

94 candidates to 64 candidates (68.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	94	9	103

Merged error: 0b

Counts

103 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
137×	`add-sqr-sqrt`
132×	`add-cube-cbrt` `*-un-lft-identity`
100×	`add-exp-log`
60×	`associate-/r*`
58×	`div-exp`
52×	`add-cbrt-cube`
26×	`cbrt-undiv`
16×	`prod-exp` `div-inv`
13×	`associate-l`
8×	`rec-exp` `1-exp` `cbrt-unprod`
7×	`pow1` `associate-/l*`
4×	`associate-/r/` `add-log-exp`
3×	`frac-2neg` `associate-r` `clear-num`
2×	`associate-*l/` `unswap-sqr`
1×	`pow-flip` `pow-prod-down` `*-commutative` `associate-/l/` `inv-pow`

Counts

4 → 266

Calls

4 calls:

4.0ms	(/ (sin (* x 0.5)) (sin x))
6.0ms	(/ 1 (/ (sin (* x 0.5)) (sin x)))
19.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin (* x 0.5)) (sin x))))
7.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

series196.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (sin (* x 0.5)) (sin x))
44.0ms	(/ 1 (/ (sin (* x 0.5)) (sin x)))
79.0ms	(/ (* (/ 8.0 3.0) (sin (* x 0.5))) (/ 1 (/ (sin (* x 0.5)) (sin x))))
36.0ms	(* (/ 8.0 3.0) (sin (* x 0.5)))

simplify64.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1121	3262
1	5001	2801

prune589.0ms

Filtered

278 candidates to 174 candidates (62.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	276	2	278
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	278	9	287

Merged error: 0b

Counts

287 → 9

regimes38.0ms

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

sample1.6s

Algorithm

intervals

Results

690.0ms	1454×	body	1280	valid
358.0ms	1234×	body	640	valid
271.0ms	4289×	body	80	valid
148.0ms	696×	body	320	valid
45.0ms	327×	body	160	valid