Details

Time bar (total: 6.6s)

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

sample66.0ms

Algorithm
intervals
Results
17.0ms194×body80valid
15.0ms31×body1280valid
6.0ms70×body80invalid
5.0ms16×body640valid
3.0ms7×body1280invalid
2.0ms9×body320valid
1.0ms4×body640invalid
1.0ms5×body320invalid
1.0ms6×body160valid
0.0ms2×body160invalid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (64.0ms)

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: 29.1b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
2.9b
(* (* x (pow s 2.0)) x)
10.3b
(* x (pow s 2.0))
19.2b
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×add-cube-cbrt *-un-lft-identity
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×cbrt-undiv add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 115
Calls
4 calls:
10.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.0ms
(* (* x (pow s 2.0)) x)
5.0ms
(* x (pow s 2.0))
9.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

series222.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
31.0ms
(* (* x (pow s 2.0)) x)
30.0ms
(* x (pow s 2.0))
82.0ms
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

simplify65.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049651594
149651594

prune236.0ms

Filtered
72 candidates to 127 candidates (-76.4%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New11611127
Fresh101
Picked101
Done000
Total11811129

Merged error: 11.7b

Counts
129 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
6.7b
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
7.6b
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))
10.3b
(* x (pow s 2.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
226×add-exp-log
202×prod-exp
50×pow-to-exp pow-exp
34×add-cbrt-cube
20×cbrt-unprod
17×add-sqr-sqrt
16×associate-*r*
14×associate-*l*
12×add-cube-cbrt *-un-lft-identity
10×unpow-prod-down
6×pow1
4×*-commutative add-log-exp sqr-pow
3×unswap-sqr
1×pow-prod-down
Counts
4 → 146
Calls
4 calls:
9.0ms
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
12.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
7.0ms
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))
5.0ms
(* x (pow s 2.0))

series225.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
80.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
52.0ms
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))
33.0ms
(* x (pow s 2.0))

simplify62.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
049921911
149921911

prune307.0ms

Filtered
71 candidates to 158 candidates (-122.5%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New14810158
Fresh3710
Picked101
Done000
Total15217169

Merged error: 8.6b

Counts
169 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
3.2b
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
6.7b
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
7.6b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
1442×add-exp-log
1342×prod-exp
354×pow-to-exp pow-exp
124×div-exp
74×add-cbrt-cube
46×cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l*
9×associate-*r*
6×pow1 cbrt-undiv unpow-prod-down
4×add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×frac-2neg pow-prod-down clear-num associate-/r* div-inv
Counts
4 → 406
Calls
4 calls:
22.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
15.0ms
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
18.0ms
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
11.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

series272.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))))
60.0ms
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
81.0ms
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
53.0ms
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

simplify143.0ms

Algorithm
egg-herbie
Counts
418 → 418
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049638463
149638463

prune287.0ms

Filtered
70 candidates to 418 candidates (-497.1%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New4126418
Fresh61016
Picked011
Done000
Total41817435

Merged error: 4.1b

Counts
435 → 17

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))))
3.2b
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
4.3b
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
6.7b
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
1496×add-exp-log
1387×prod-exp
356×pow-to-exp pow-exp
127×div-exp
92×add-cbrt-cube
59×cbrt-unprod
11×pow1 associate-*l*
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×cbrt-undiv
4×pow-prod-down add-log-exp
3×unpow-prod-down times-frac associate-*r* *-commutative associate-/l*
1×frac-2neg clear-num associate-/r* div-inv sqr-pow
Counts
4 → 414
Calls
4 calls:
25.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))))
13.0ms
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
10.0ms
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
19.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

series267.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (cos (* 2.0 x)) (* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))))
59.0ms
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
53.0ms
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
78.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

simplify90.0ms

Algorithm
egg-herbie
Counts
426 → 426
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
054938937

prune194.0ms

Filtered
66 candidates to 426 candidates (-545.5%)
Pruning

19 alts after pruning (17 fresh and 2 done)

PrunedKeptTotal
New4233426
Fresh11415
Picked011
Done011
Total42419443

Merged error: 3.7b

Counts
443 → 19

regimes806.0ms

Accuracy

29% (4.6b remaining)

Error of 7.6b against oracle of 3.0b and baseline of 9.5b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040108
140108

end0.0ms

sample1.9s

Algorithm
intervals
Results
539.0ms5971×body80valid
337.0ms706×body1280valid
247.0ms716×body640valid
163.0ms1890×body80invalid
110.0ms417×body320valid
85.0ms252×body640invalid
70.0ms145×body1280invalid
47.0ms172×body320invalid
33.0ms190×body160valid
18.0ms112×body160invalid

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