Details

Time bar (total: 6.5s)

analyze1.0s

Algorithm
search
Search
TrueOtherFalseIter
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

sample71.0ms

Algorithm
intervals
Results
17.0ms28×body1280valid
17.0ms191×body80valid
7.0ms21×body640valid
6.0ms70×body80invalid
3.0ms7×body1280invalid
2.0ms9×body320valid
2.0ms6×body640invalid
1.0ms7×body160valid
1.0ms5×body320invalid
0.0ms2×body160invalid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0484516
1484516

prune12.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 24.7b

Counts
2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(cos (* 2.0 x))
4.6b
(* x (* x (* (pow c 2.0) (pow s 2.0))))
7.1b
(* x (* (pow c 2.0) (pow s 2.0)))
15.0b
(* (pow c 2.0) (pow s 2.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
74×add-exp-log
58×prod-exp
22×add-sqr-sqrt
20×add-cbrt-cube
18×pow-to-exp pow-exp
13×associate-*l*
12×unpow-prod-down
11×pow1
10×add-cube-cbrt *-un-lft-identity cbrt-unprod
9×associate-*r* unswap-sqr
8×sqr-pow
5×pow-prod-down
4×add-log-exp
3×*-commutative
Counts
4 → 102
Calls
4 calls:
2.0ms
(cos (* 2.0 x))
9.0ms
(* 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))

series175.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(cos (* 2.0 x))
60.0ms
(* x (* x (* (pow c 2.0) (pow s 2.0))))
52.0ms
(* x (* (pow c 2.0) (pow s 2.0)))
60.0ms
(* (pow c 2.0) (pow s 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
050561080

prune219.0ms

Filtered
71 candidates to 114 candidates (-60.6%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10311114
Fresh011
Picked101
Done000
Total10412116

Merged error: 11.4b

Counts
116 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
0.5b
(cos (* 2.0 x))
4.6b
(* x (* x (pow (* c s) 2.0)))
7.1b
(* x (pow (* c s) 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
47×add-exp-log
25×prod-exp
20×add-cbrt-cube
12×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
7×cbrt-unprod
6×pow1 div-exp associate-*r* associate-*l* pow-exp
4×add-log-exp
3×cbrt-undiv pow-to-exp times-frac associate-/l*
2×*-commutative unswap-sqr sqr-pow
1×unpow-prod-down frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 76
Calls
4 calls:
9.0ms
(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
2.0ms
(cos (* 2.0 x))
5.0ms
(* x (* x (pow (* c s) 2.0)))
5.0ms
(* x (pow (* c s) 2.0))

series172.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
2.0ms
(cos (* 2.0 x))
56.0ms
(* x (* x (pow (* c s) 2.0)))
47.0ms
(* x (pow (* c s) 2.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
050301049

prune192.0ms

Filtered
58 candidates to 88 candidates (-51.7%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New771188
Fresh8311
Picked101
Done000
Total8614100

Merged error: 4.6b

Counts
100 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2)))))
0.5b
(cos (* 2.0 x))
4.6b
(* x (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2))))
4.9b
(* x (pow (* c s) (/ 2.0 2)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
191×add-exp-log
137×prod-exp
38×pow-exp
29×add-cbrt-cube
22×div-exp
19×pow-to-exp
13×cbrt-unprod
12×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity
6×pow1 associate-*r* associate-*l*
4×cbrt-undiv add-log-exp
3×times-frac associate-/l*
2×*-commutative unswap-sqr sqr-pow
1×unpow-prod-down frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 110
Calls
4 calls:
11.0ms
(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2)))))
2.0ms
(cos (* 2.0 x))
9.0ms
(* x (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2))))
5.0ms
(* x (pow (* c s) (/ 2.0 2)))

series173.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2)))))
2.0ms
(cos (* 2.0 x))
53.0ms
(* x (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2))))
50.0ms
(* x (pow (* c s) (/ 2.0 2)))

simplify43.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
055191751

prune220.0ms

Filtered
62 candidates to 122 candidates (-96.8%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1166122
Fresh6713
Picked101
Done000
Total12313136

Merged error: 2.5b

Counts
136 → 13

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2)))
0.5b
(cos (* x 2.0))
4.6b
(/ (/ (cos (* x 2.0)) x) (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2))))
4.9b
(* x (pow (* c s) (/ 2.0 2)))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
245×add-exp-log
140×prod-exp
63×div-exp
56×pow-exp
32×add-cbrt-cube
31×times-frac
28×pow-to-exp
24×add-sqr-sqrt
21×add-cube-cbrt *-un-lft-identity
13×associate-/l*
10×associate-*r* cbrt-unprod
9×cbrt-undiv
4×pow1 associate-*l* add-log-exp
3×div-inv sqr-pow
2×unpow-prod-down *-commutative unswap-sqr
1×frac-2neg clear-num associate-/r* associate-/l/
Counts
4 → 152
Calls
4 calls:
8.0ms
(* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2)))
2.0ms
(cos (* x 2.0))
11.0ms
(/ (/ (cos (* x 2.0)) x) (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2))))
5.0ms
(* x (pow (* c s) (/ 2.0 2)))

series168.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2)))
2.0ms
(cos (* x 2.0))
69.0ms
(/ (/ (cos (* x 2.0)) x) (* (* x (pow (* c s) (/ 2.0 2))) (pow (* c s) (/ 2.0 2))))
50.0ms
(* x (pow (* c s) (/ 2.0 2)))

simplify54.0ms

Algorithm
egg-herbie
Counts
164 → 164
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
057272682

prune205.0ms

Filtered
80 candidates to 164 candidates (-105.0%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New1595164
Fresh7512
Picked011
Done000
Total16611177

Merged error: 2.5b

Counts
177 → 11

regimes482.0ms

Accuracy

0% (1.1b remaining)

Error of 3.4b against oracle of 2.3b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02241
12241

end0.0ms

analyze1.0s

Algorithm
search
Search
TrueOtherFalseIter
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

sample2.0s

Algorithm
intervals
Results
542.0ms5988×body80valid
338.0ms669×body1280valid
269.0ms743×body640valid
176.0ms1927×body80invalid
110.0ms383×body320valid
72.0ms216×body640invalid
67.0ms134×body1280invalid
48.0ms197×body320invalid
43.0ms217×body160valid
16.0ms94×body160invalid

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