Details

Time bar (total: 6.7s)

analyze1.2s

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

sample67.0ms

Algorithm
intervals
Results
17.0ms191×body80valid
12.0ms27×body640valid
11.0ms22×body1280valid
5.0ms60×body80invalid
4.0ms13×body320valid
2.0ms4×body1280invalid
1.0ms3×body640invalid
1.0ms5×body160invalid
1.0ms3×body320invalid
1.0ms3×body160valid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
0484516
1484516

prune13.0ms

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: 24.4b

Counts
2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
5.1b
(* (* x (pow s 2.0)) x)
7.9b
(* x (pow s 2.0))
18.1b
(* (pow c 2.0) (* (* x (pow s 2.0)) x))

rewrite38.0ms

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:
14.0ms
(/ (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))

series229.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(/ (cos (* 2.0 x)) (* (pow c 2.0) (* (* x (pow s 2.0)) x)))
32.0ms
(* (* x (pow s 2.0)) x)
34.0ms
(* 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

prune253.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New11512127
Fresh101
Picked101
Done000
Total11712129

Merged error: 12.0b

Counts
129 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

5.2b
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
5.5b
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
7.9b
(* x (pow s 2.0))
9.0b
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

rewrite41.0ms

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)))))
5.0ms
(* x (pow s 2.0))
7.0ms
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

series230.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2))))
82.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s 2.0)) (pow c (/ 2.0 2)))))
31.0ms
(* x (pow s 2.0))
57.0ms
(* (* x (pow s 2.0)) (pow c (/ 2.0 2)))

simplify59.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049921911
149921911

prune283.0ms

Filtered
70 candidates to 158 candidates (-125.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1508158
Fresh6511
Picked101
Done000
Total15713170

Merged error: 9.9b

Counts
170 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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))))))
5.2b
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
5.5b
(* (pow c (/ 2.0 2)) (* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))))
9.0b
(* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

rewrite109.0ms

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:
23.0ms
(/ (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))))))
13.0ms
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
17.0ms
(* (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)))

series284.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(/ (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))))))
63.0ms
(* x (* (* (* x (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2))))
82.0ms
(* (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 (pow s (/ 2.0 2))) (pow s (/ 2.0 2))) (pow c (/ 2.0 2)))

simplify138.0ms

Algorithm
egg-herbie
Counts
418 → 418
Iterations

Useful iterations: 0 (89.0ms)

IterNodesCost
049638463
149638463

prune298.0ms

Filtered
68 candidates to 418 candidates (-514.7%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New4126418
Fresh3912
Picked011
Done000
Total41516431

Merged error: 4.9b

Counts
431 → 16

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (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)))))))
3.7b
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
5.2b
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
5.5b
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

rewrite116.0ms

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:
24.0ms
(/ (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)))))))
10.0ms
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
14.0ms
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
21.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

series280.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ (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)))))))
56.0ms
(* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))
62.0ms
(* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2)))))
85.0ms
(* (pow c (/ 2.0 2)) (* x (* (* x (pow s (/ 2.0 2))) (* (pow c (/ 2.0 2)) (pow s (/ 2.0 2))))))

simplify91.0ms

Algorithm
egg-herbie
Counts
426 → 426
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
054938937

prune208.0ms

Filtered
65 candidates to 426 candidates (-555.4%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New4233426
Fresh31114
Picked101
Done101
Total42814442

Merged error: 3.7b

Counts
442 → 14

regimes696.0ms

Accuracy

30.5% (4.6b remaining)

Error of 7.6b against oracle of 3.0b and baseline of 9.6b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
040108
140108

end0.0ms

sample1.9s

Algorithm
intervals
Results
526.0ms5994×body80valid
337.0ms671×body1280valid
272.0ms755×body640valid
162.0ms1867×body80invalid
107.0ms392×body320valid
83.0ms245×body640invalid
69.0ms135×body1280invalid
41.0ms174×body320invalid
33.0ms188×body160valid
18.0ms110×body160invalid

Profiling

Loading profile data...