Details

sample206.0ms

Algorithm

intervals

Results

104.0ms	91×	body	1280	valid
47.0ms	57×	body	640	valid
13.0ms	23×	body	320	valid
12.0ms	73×	body	80	valid
4.0ms	12×	body	160	valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	74	30
1	182	30
2	657	30
3	2727	30
4	5001	30

prune5.0ms

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: 0.5b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b	(- 3.0 (sqrt 5.0))
1.3b	(- (cos x) (cos y))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`associate-r`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
10×	`associate-*r/`
9×	`flip3--` `flip--`
8×	`add-cube-cbrt` `add-log-exp`
7×	`associate-l` `difference-of-squares`
6×	`sub-neg`
5×	`sqrt-prod`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
2×	`times-frac` `diff-log` `associate-l/` `-commutative` `unswap-sqr`
1×	`diff-cos`

Counts

4 → 94

Calls

4 calls:

17.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- 3.0 (sqrt 5.0))
4.0ms	(- (cos x) (cos y))

series269.0ms

Counts

4 → 10

Calls

4 calls:

131.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
85.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms	(- 3.0 (sqrt 5.0))
53.0ms	(- (cos x) (cos y))

simplify65.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	622	1094
1	2643	1002
2	5003	1002

prune519.0ms

Filtered

104 candidates to 70 candidates (67.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.3b

Counts

105 → 8

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.3b	(- (cos x) (cos y))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
29×	`associate-l`
21×	`times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
15×	`associate-r`
13×	`pow1`
11×	`difference-of-squares`
10×	`associate-*r/`
8×	`flip3--` `flip--`
7×	`sqrt-prod`
6×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp`
5×	`sub-neg` `pow-prod-down`
4×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `unswap-sqr`
3×	`associate-l/` `-commutative`
1×	`cbrt-undiv` `diff-log` `div-exp` `div-inv` `diff-cos`

Counts

4 → 120

Calls

4 calls:

11.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
18.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
12.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
5.0ms	(- (cos x) (cos y))

series358.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))
128.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
86.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
56.0ms	(- (cos x) (cos y))

simplify86.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	751	1321
1	3282	1206
2	5001	1206

prune793.0ms

Filtered

132 candidates to 89 candidates (67.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	122	10	132
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	125	15	140

Merged error: 0.2b

Counts

140 → 15

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
0.3b	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
0.3b	(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
1.3b	(- (cos x) (cos y))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
21×	`sqrt-prod`
20×	`pow1` `add-exp-log` `associate-*r/` `add-cbrt-cube`
19×	`associate-l`
18×	`*-un-lft-identity`
13×	`associate-r`
12×	`distribute-rgt-in` `add-cube-cbrt` `distribute-lft-in`
10×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`sub-neg` `flip3--` `flip--`
6×	`add-log-exp`
5×	`difference-of-squares`
4×	`frac-times`
3×	`*-commutative` `distribute-lft-out--` `unswap-sqr`
2×	`times-frac` `associate-*l/`
1×	`diff-log` `diff-cos`

Counts

4 → 120

Calls

4 calls:

22.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
15.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
15.0ms	(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
4.0ms	(- (cos x) (cos y))

series392.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(* (* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))) (- (sin y) (/ (sin x) 16.0)))
89.0ms	(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0))))
113.0ms	(* (sqrt (sqrt 2.0)) (- (sin x) (/ (sin y) 16.0)))
55.0ms	(- (cos x) (cos y))

simplify83.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	637	1601
1	3053	1361
2	5003	1361

prune781.0ms

Filtered

132 candidates to 84 candidates (63.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	133	14	147

Merged error: 0.2b

Counts

147 → 14

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
0.4b	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.7b	(* (/ (sqrt (- (sqrt 5.0) 1.0)) 1) (* (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0) (cos x)))
1.3b	(- (cos x) (cos y))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
41×	`add-exp-log`
38×	`associate-l`
36×	`*-un-lft-identity`
32×	`add-cbrt-cube`
29×	`times-frac`
25×	`sqrt-prod`
24×	`add-cube-cbrt`
19×	`prod-exp`
16×	`pow1`
14×	`cbrt-unprod`
13×	`associate-r`
11×	`associate-*r/` `difference-of-squares`
9×	`div-exp`
8×	`flip3--` `flip--`
7×	`pow-prod-down`
6×	`distribute-lft-out--` `add-log-exp`
5×	`cbrt-undiv` `frac-times` `sub-neg` `associate-*l/`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`1-exp` `*-commutative`
2×	`unswap-sqr`
1×	`diff-log` `div-inv` `diff-cos`

Counts

4 → 139

Calls

4 calls:

18.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
11.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
20.0ms	(* (/ (sqrt (- (sqrt 5.0) 1.0)) 1) (* (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0) (cos x)))
7.0ms	(- (cos x) (cos y))

series376.0ms

Counts

4 → 12

Calls

4 calls:

136.0ms	(* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0)))
88.0ms	(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
93.0ms	(* (/ (sqrt (- (sqrt 5.0) 1.0)) 1) (* (/ (sqrt (- (sqrt 5.0) 1.0)) 2.0) (cos x)))
58.0ms	(- (cos x) (cos y))

simplify112.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	903	1804
1	4346	1532
2	5002	1424

prune813.0ms

Filtered

151 candidates to 95 candidates (62.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	151	14	165

Merged error: 0.2b

Counts

165 → 14

regimes244.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	52
1	60	52
2	60	52

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.9s	2781×	body	1280	valid
1.2s	1840×	body	640	valid
354.0ms	756×	body	320	valid
319.0ms	2310×	body	80	valid
103.0ms	313×	body	160	valid