Details

Time bar (total: 6.9s)

analyze990.0ms

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

sample211.0ms

Algorithm
intervals
Results
150.0ms56×body80invalid
15.0ms182×body80valid
11.0ms33×body640valid
10.0ms21×body1280valid
4.0ms14×body320valid
3.0ms10×body640invalid
2.0ms5×body1280invalid
1.0ms5×body320invalid
1.0ms6×body160valid
0.0ms3×body160invalid

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (66.0ms)

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: 25.3b

Counts
2 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
4.3b
(* x (* x (* (pow c 2.0) (pow s 2.0))))
7.5b
(* x (* (pow c 2.0) (pow s 2.0)))
18.4b
(* (pow c 2.0) (pow s 2.0))

rewrite37.0ms

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:
10.0ms
(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
9.0ms
(* x (* x (* (pow c 2.0) (pow s 2.0))))
6.0ms
(* x (* (pow c 2.0) (pow s 2.0)))
6.0ms
(* (pow c 2.0) (pow s 2.0))

series245.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* x (* x (* (pow c 2.0) (pow s 2.0)))))
59.0ms
(* x (* x (* (pow c 2.0) (pow s 2.0))))
51.0ms
(* x (* (pow c 2.0) (pow s 2.0)))
59.0ms
(* (pow c 2.0) (pow s 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
049561811
149561811

prune260.0ms

Filtered
82 candidates to 140 candidates (-70.7%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New12911140
Fresh011
Picked101
Done000
Total13012142

Merged error: 8.5b

Counts
142 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
0.3b
(pow (* c s) 2.0)
4.3b
(* x (* x (pow (* c s) 2.0)))
7.5b
(* x (pow (* c s) 2.0))

rewrite23.0ms

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:
7.0ms
(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
3.0ms
(pow (* c s) 2.0)
5.0ms
(* x (* x (pow (* c s) 2.0)))
5.0ms
(* x (pow (* c s) 2.0))

series182.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ (cos (* 2.0 x)) (* x (* x (pow (* c s) 2.0))))
14.0ms
(pow (* c s) 2.0)
54.0ms
(* x (* x (pow (* c s) 2.0)))
46.0ms
(* x (pow (* c s) 2.0))

simplify70.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049511113
149511113

prune214.0ms

Filtered
62 candidates to 98 candidates (-58.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New881098
Fresh5611
Picked101
Done000
Total9416110

Merged error: 3.5b

Counts
110 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
0.2b
(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
3.7b
(* x (pow (* c s) (* 1/2 2.0)))
4.3b
(* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

rewrite39.0ms

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:
11.0ms
(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
7.0ms
(* (* 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))))

series220.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (cos (* 2.0 x)) (* x (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))))
49.0ms
(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
46.0ms
(* 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))))

simplify50.0ms

Algorithm
egg-herbie
Counts
151 → 151
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
054661843

prune209.0ms

Filtered
63 candidates to 151 candidates (-139.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1447151
Fresh6915
Picked101
Done000
Total15116167

Merged error: 1.3b

Counts
167 → 16

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cos (* x 2.0)) x)
0.2b
(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
3.7b
(* x (pow (* c s) (* 1/2 2.0)))
4.3b
(/ (/ (cos (* x 2.0)) x) (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
247×add-exp-log
140×prod-exp
64×div-exp
56×pow-exp
40×times-frac
34×add-cbrt-cube
32×add-sqr-sqrt
29×add-cube-cbrt *-un-lft-identity
28×pow-to-exp
16×associate-/l*
10×cbrt-undiv associate-*r* cbrt-unprod
4×pow1 associate-*l* associate-/r* div-inv add-log-exp
3×sqr-pow
2×unpow-prod-down frac-2neg clear-num *-commutative unswap-sqr
1×associate-/l/
Counts
4 → 172
Calls
4 calls:
3.0ms
(/ (cos (* x 2.0)) x)
8.0ms
(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
5.0ms
(* x (pow (* c s) (* 1/2 2.0)))
12.0ms
(/ (/ (cos (* x 2.0)) x) (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

series167.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ (cos (* x 2.0)) x)
46.0ms
(* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2)))
46.0ms
(* x (pow (* c s) (* 1/2 2.0)))
69.0ms
(/ (/ (cos (* x 2.0)) x) (* (* x (pow (* c s) (* 1/2 2.0))) (pow (* c s) (/ 2.0 2))))

simplify78.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 0 (61.0ms)

IterNodesCost
049492561
149492561

prune240.0ms

Filtered
97 candidates to 184 candidates (-89.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New1777184
Fresh6915
Picked101
Done000
Total18416200

Merged error: 1.3b

Counts
200 → 16

regimes627.0ms

Accuracy

0% (0.5b remaining)

Error of 2.6b against oracle of 2.1b and baseline of 2.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02126
12126

end0.0ms

analyze983.0ms

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

sample1.9s

Algorithm
intervals
Results
525.0ms6028×body80valid
311.0ms639×body1280valid
257.0ms747×body640valid
162.0ms1838×body80invalid
97.0ms389×body320valid
76.0ms243×body640invalid
65.0ms135×body1280invalid
46.0ms199×body320invalid
34.0ms197×body160valid
18.0ms112×body160invalid

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