Details

Time bar (total: 11.6s)

analyze1.4s

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

sample217.0ms

Algorithm
intervals
Results
146.0ms126×body1280valid
40.0ms58×body640valid
9.0ms20×body320valid
6.0ms42×body80valid
3.0ms10×body160valid

simplify60.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0476616
1476616

prune17.0ms

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: 3.2b

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))
0.2b
(pow (sin ky) 2.0)
0.2b
(pow (sin kx) 2.0)
3.0b
(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 ky) 2.0)
3.0ms
(pow (sin kx) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series103.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms
(pow (sin ky) 2.0)
22.0ms
(pow (sin kx) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify77.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
052281477

prune264.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10211113
Fresh011
Picked101
Done000
Total10312115

Merged error: 2.3b

Counts
115 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.2b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b
(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:
3.0ms
(pow (sin kx) 2.0)
11.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
17.0ms
(* (sin ky) (/ (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)))

series124.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin kx) 2.0)
40.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
46.0ms
(* (sin ky) (/ (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)))

simplify84.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
050582219

prune264.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1414145
Fresh4711
Picked011
Done000
Total14512157

Merged error: 2.3b

Counts
157 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
0.3b
(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
0.3b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
370×times-frac
293×*-un-lft-identity
208×add-sqr-sqrt
186×add-cube-cbrt
132×sqrt-prod
89×associate-*r*
52×unpow-prod-down distribute-lft-out
36×add-exp-log
31×associate-/r*
20×add-cbrt-cube
15×div-exp
11×associate-/l*
10×div-inv
8×pow1
7×cbrt-undiv prod-exp unswap-sqr
4×rec-exp sqrt-div 1-exp add-log-exp
3×associate-*l* cbrt-unprod
2×frac-2neg flip3-+ clear-num associate-/r/ flip-+ associate-/l/
1×rem-sqrt-square pow-flip sqrt-pow1 pow1/2 associate-*r/ pow-prod-down un-div-inv *-commutative inv-pow
Counts
4 → 322
Calls
4 calls:
11.0ms
(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
30.0ms
(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
14.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series142.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))
47.0ms
(* (sin ky) (/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th))))
41.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin th)))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify96.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049576414
149576414

prune536.0ms

Filtered
164 candidates to 334 candidates (-103.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New3340334
Fresh01010
Picked011
Done011
Total33412346

Merged error: 2.3b

Counts
346 → 12

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(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)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series109.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(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

prune471.0ms

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

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1020102
Fresh099
Picked011
Done022
Total10212114

Merged error: 2.3b

Counts
114 → 12

regimes850.0ms

Accuracy

0% (1.4b remaining)

Error of 4.0b against oracle of 2.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01516
11516

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.2s3667×body1280valid
1.5s2007×body640valid
369.0ms750×body320valid
176.0ms1260×body80valid
96.0ms316×body160valid

Profiling

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