Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample64.0ms

Algorithm

intervals

Results

17.0ms	202×	body	80	valid
11.0ms	23×	body	1280	valid
7.0ms	19×	body	640	valid
5.0ms	64×	body	80	invalid
3.0ms	9×	body	640	invalid
3.0ms	9×	body	320	valid
2.0ms	5×	body	1280	invalid
1.0ms	3×	body	320	invalid
1.0ms	3×	body	160	valid
0.0ms	1×	body	160	invalid

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5005	16

prune19.0ms

Filtered

1 candidates to 1 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: 26.5b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
5.1b	(* x (* x (* (pow c 2.0) (pow s 2.0))))
8.3b	(* x (* (pow c 2.0) (pow s 2.0)))
16.8b	(* (pow c 2.0) (pow s 2.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log`
88×	`prod-exp`
34×	`add-cbrt-cube`
24×	`add-sqr-sqrt` `pow-to-exp` `pow-exp`
16×	`cbrt-unprod`
13×	`associate-l`
12×	`add-cube-cbrt` `unpow-prod-down` `*-un-lft-identity` `div-exp`
11×	`pow1`
9×	`associate-r` `unswap-sqr`
8×	`sqr-pow`
5×	`pow-prod-down`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 128

Calls

4 calls:

11.0ms	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
10.0ms	(* x (* x (* (pow c 2.0) (pow s 2.0))))
7.0ms	(* x (* (pow c 2.0) (pow s 2.0)))
7.0ms	(* (pow c 2.0) (pow s 2.0))

series254.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
61.0ms	(* x (* x (* (pow c 2.0) (pow s 2.0))))
54.0ms	(* x (* (pow c 2.0) (pow s 2.0)))
60.0ms	(* (pow c 2.0) (pow s 2.0))

simplify61.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5007	1819

prune277.0ms

Filtered

82 candidates to 140 candidates (-70.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	128	12	140
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	129	13	142

Merged error: 8.6b

Counts

142 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* c s) 2.0)
0.3b	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
5.1b	(* x (* x (pow (* c s) 2.0)))
8.3b	(* x (pow (* c s) 2.0))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
26×	`prod-exp`
20×	`add-cbrt-cube`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`pow-exp`
7×	`cbrt-unprod`
6×	`div-exp` `associate-r` `associate-l`
4×	`pow-to-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `times-frac` `associate-/l*` `sqr-pow`
2×	`unpow-prod-down` `pow-pow` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 86

Calls

4 calls:

4.0ms	(pow (* c s) 2.0)
8.0ms	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
6.0ms	(* x (* x (pow (* c s) 2.0)))
5.0ms	(* x (pow (* c s) 2.0))

series184.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(pow (* c s) 2.0)
68.0ms	(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
54.0ms	(* x (* x (pow (* c s) 2.0)))
48.0ms	(* x (pow (* c s) 2.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5025	1115

prune209.0ms

Filtered

62 candidates to 98 candidates (-58.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	99	12	111

Merged error: 3.6b

Counts

111 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
0.3b	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
4.0b	(* x (pow (* c s) (* 1/2 2.0)))
5.1b	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log`
182×	`prod-exp`
56×	`pow-exp`
34×	`add-cbrt-cube`
28×	`pow-to-exp`
22×	`div-exp`
16×	`cbrt-unprod`
13×	`add-sqr-sqrt`
11×	`associate-r`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-l`
6×	`pow1`
4×	`cbrt-undiv` `add-log-exp`
3×	`times-frac` `-commutative` `associate-/l` `sqr-pow`
2×	`unpow-prod-down` `unswap-sqr`
1×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 139

Calls

4 calls:

8.0ms	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
11.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
5.0ms	(* x (pow (* c s) (* 1/2 2.0)))
9.0ms	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

series223.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
70.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
47.0ms	(* x (pow (* c s) (* 1/2 2.0)))
58.0ms	(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4971	1844
1	4971	1844

prune228.0ms

Filtered

67 candidates to 151 candidates (-125.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	143	8	151
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	150	13	163

Merged error: 0.9b

Counts

163 → 13

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (cos (* 2.0 x)) (* x (* (* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2)))))
0.3b	(/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0)))
4.0b	(* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0))
5.1b	(* x (* (* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2))))

rewrite566.0ms

Algorithm

rewrite-expression-head

Rules

9839×	`add-exp-log`
7360×	`pow-exp`
7286×	`prod-exp`
3058×	`div-exp`
1367×	`pow-to-exp`
1130×	`rec-exp` `1-exp`
34×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
14×	`cbrt-unprod`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`associate-r`
9×	`times-frac`
8×	`unpow-prod-down`
7×	`pow1`
6×	`cbrt-undiv` `associate-l` `associate-/l*`
4×	`add-log-exp`
3×	`div-inv` `unswap-sqr`
2×	`pow-flip` `frac-2neg` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `sqr-pow`
1×	`inv-pow`

Counts

4 → 2073

Calls

4 calls:

98.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2)))))
28.0ms	(/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0)))
27.0ms	(* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0))
70.0ms	(* x (* (* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2))))

series261.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(/ (cos (* 2.0 x)) (* x (* (* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2)))))
59.0ms	(/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0)))
56.0ms	(* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0))
70.0ms	(* x (* (* x (pow (/ 1 (* (pow (pow (/ 1 c) 1.0) 1.0) (pow (pow (/ 1 s) 1.0) 1.0))) 1.0)) (pow (* c s) (/ 2.0 2))))

simplify508.0ms

Algorithm

egg-herbie

Counts

2085 → 2085

Iterations

Useful iterations: 0 (225.0ms)

Iter	Nodes	Cost
0	5101	49543

prune376.0ms

Filtered

87 candidates to 2085 candidates (-2296.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	2082	3	2085
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	2082	16	2098

Merged error: 0.9b

Counts

2098 → 16

regimes621.0ms

Accuracy

34.3% (2.7b remaining)

Error of 5.1b against oracle of 2.4b and baseline of 6.5b

bsearch158.0ms

Steps

Iters	Range	Point
9	8.798093072247463e+135	3.03502477725236e+143	2.118882394209553e+141
10	1.913252361237017e-218	3.7250395666460526e-204	4.3509914516597875e-206
10	-2.8569580159337343e-192	-8.703759963336767e-209	-1.3315982683246538e-194

Iters

Range

Point

8.798093072247463e+135

3.03502477725236e+143

2.118882394209553e+141

1.913252361237017e-218

3.7250395666460526e-204

4.3509914516597875e-206

-2.8569580159337343e-192

-8.703759963336767e-209

-1.3315982683246538e-194

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	192	130
1	192	130

end0.0ms

sample1.9s

Algorithm

intervals

Results

530.0ms	5993×	body	80	valid
332.0ms	699×	body	1280	valid
251.0ms	716×	body	640	valid
167.0ms	1914×	body	80	invalid
103.0ms	385×	body	320	valid
79.0ms	250×	body	640	invalid
64.0ms	126×	body	1280	invalid
45.0ms	197×	body	320	invalid
35.0ms	207×	body	160	valid
17.0ms	105×	body	160	invalid

Details

analyze1.1s

sample64.0ms

simplify66.0ms

prune19.0ms

localize14.0ms

rewrite40.0ms

series254.0ms

simplify61.0ms

prune277.0ms

localize11.0ms

rewrite24.0ms

series184.0ms

simplify55.0ms

prune209.0ms

localize17.0ms

rewrite41.0ms

series223.0ms

simplify61.0ms

prune228.0ms

localize28.0ms

rewrite566.0ms

series261.0ms

simplify508.0ms

prune376.0ms

regimes621.0ms

bsearch158.0ms

simplify3.0ms

end0.0ms

sample1.9s

Profiling