Details

Time bar (total: 11.1s)

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
0%99.9%0.1%7
25%74.9%0.1%8
54.6%45.2%0.1%9
56.2%43.7%0.1%10
62.4%37.4%0.1%11
65.9%33.9%0.1%12
66.3%33.5%0.1%13
69%30.8%0.1%14

sample195.0ms

Algorithm
intervals
Results
118.0ms111×body1280valid
44.0ms61×body640valid
12.0ms26×body320valid
6.0ms50×body80valid
2.0ms8×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0476616
1476616

prune18.0ms

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: 3.7b

Counts
2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
34×add-sqr-sqrt
30×associate-*l*
26×times-frac
25×add-cube-cbrt
21×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×pow1 add-cbrt-cube
8×distribute-lft-out
6×pow-unpow
4×sqrt-div add-log-exp
3×associate-*r* unswap-sqr
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
16.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series106.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms
(pow (sin kx) 2.0)
22.0ms
(pow (sin ky) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify76.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
052281477

prune275.0ms

Filtered
77 candidates to 113 candidates (-46.8%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New10013113
Fresh011
Picked101
Done000
Total10114115

Merged error: 2.1b

Counts
115 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
41×sqrt-prod
40×add-cube-cbrt
30×associate-*r*
19×unpow-prod-down
16×distribute-lft-out
12×add-exp-log
11×add-cbrt-cube
8×pow1 associate-/r*
6×sqrt-div
4×associate-/r/ add-log-exp
3×pow-unpow flip3-+ associate-*l* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down pow-exp clear-num *-commutative sqr-pow
Counts
4 → 133
Calls
4 calls:
2.0ms
(pow (sin ky) 2.0)
17.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
11.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
166.0ms
(pow (sin ky) 2.0)
45.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
44.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify68.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (54.0ms)

IterNodesCost
049332217
149332217

prune286.0ms

Filtered
85 candidates to 145 candidates (-70.6%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1423145
Fresh21113
Picked101
Done000
Total14514159

Merged error: 2.1b

Counts
159 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.4b
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
100×sqrt-prod
52×add-sqr-sqrt
50×*-un-lft-identity
34×sqrt-pow1
30×pow1
28×sqrt-div
20×add-cube-cbrt
19×swap-sqr
18×pow1/2
15×unpow-prod-down
14×distribute-lft-out
11×associate-*r* associate-*l*
9×pow-prod-up unswap-sqr
8×flip3-+ flip-+
7×add-exp-log
6×add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times add-log-exp
3×pow-unpow
2×rem-sqrt-square associate-*r/ associate-*l/
1×pow2 pow-to-exp pow-pow pow-plus sqrt-unprod pow-exp prod-exp rem-square-sqrt *-commutative cbrt-unprod sqr-pow
Counts
4 → 142
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
23.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series75.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin ky) 2.0)
19.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049322020
149322020

prune302.0ms

Filtered
72 candidates to 154 candidates (-113.9%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New1540154
Fresh01313
Picked011
Done000
Total15414168

Merged error: 2.1b

Counts
168 → 14

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
30×cbrt-prod sqrt-prod
25×add-sqr-sqrt
24×times-frac
22×add-cube-cbrt
12×unpow-prod-down distribute-lft-out
8×sqrt-div
7×pow1
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×associate-/r/
1×cbrt-div pow1/3 div-inv
Counts
4 → 90
Calls
4 calls:
12.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series112.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
055421796

prune334.0ms

Filtered
68 candidates to 102 candidates (-50.0%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1020102
Fresh01212
Picked011
Done011
Total10214116

Merged error: 2.1b

Counts
116 → 14

regimes1.2s

Accuracy

61.9% (0.7b remaining)

Error of 3.1b against oracle of 2.4b and baseline of 4.2b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04066
14066

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.9s3692×body1280valid
1.4s2075×body640valid
313.0ms692×body320valid
158.0ms1273×body80valid
73.0ms268×body160valid

Profiling

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