Details

Time bar (total: 11.5s)

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

sample220.0ms

Algorithm
intervals
Results
108.0ms105×body1280valid
50.0ms72×body640valid
9.0ms21×body320valid
5.0ms46×body80valid
3.0ms12×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (59.0ms)

IterNodesCost
0476616
1476616

prune14.0ms

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: 2.1b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b
(pow (sin kx) 2.0)
0.2b
(pow (sin ky) 2.0)
2.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
27×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
16×unpow-prod-down
10×distribute-lft-out
8×add-exp-log associate-/r*
7×pow1
6×pow-unpow add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
11.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
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)))

series100.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms
(pow (sin kx) 2.0)
19.0ms
(pow (sin ky) 2.0)
25.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify66.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
049621511
149621511

prune234.0ms

Filtered
70 candidates to 112 candidates (-60.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1039112
Fresh011
Picked101
Done000
Total10410114

Merged error: 1.0b

Counts
114 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.2b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b
(pow (sin ky) 2.0)
2.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
150×*-un-lft-identity
99×add-sqr-sqrt
98×add-cube-cbrt
65×sqrt-prod
32×unpow-prod-down
28×associate-/r*
26×distribute-lft-out
17×add-exp-log
9×add-cbrt-cube
8×pow1
7×div-exp
6×pow-unpow
5×div-inv
4×add-log-exp
3×cbrt-undiv associate-/l*
2×pow-to-exp rec-exp pow-pow sqrt-div 1-exp pow-exp sqr-pow
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 flip3-+ pow1/2 clear-num associate-/r/ flip-+ inv-pow
Counts
4 → 187
Calls
4 calls:
3.0ms
(pow (sin kx) 2.0)
14.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
3.0ms
(pow (sin ky) 2.0)
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series96.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(pow (sin kx) 2.0)
35.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
19.0ms
(pow (sin ky) 2.0)
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify67.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
050533593

prune295.0ms

Filtered
94 candidates to 199 candidates (-111.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1972199
Fresh279
Picked011
Done000
Total19910209

Merged error: 1.0b

Counts
209 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
0.2b
(pow (sin kx) 2.0)
0.2b
(pow (sin ky) 2.0)
2.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
1005×times-frac
608×*-un-lft-identity
437×add-sqr-sqrt
436×add-cube-cbrt
215×sqrt-prod
92×unpow-prod-down
86×distribute-lft-out
46×add-exp-log div-inv
32×div-exp
30×sqrt-div associate-/l*
29×associate-/r/
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv rec-exp 1-exp
7×pow1
6×pow-unpow
4×add-log-exp
2×pow-to-exp pow-pow pow-exp sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 516
Calls
4 calls:
26.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series100.0ms

Counts
4 → 12
Calls
4 calls:
35.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
19.0ms
(pow (sin kx) 2.0)
19.0ms
(pow (sin ky) 2.0)
26.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify173.0ms

Algorithm
egg-herbie
Counts
528 → 528
Iterations

Useful iterations: 0 (93.0ms)

IterNodesCost
0495613846
1495613846

prune646.0ms

Filtered
176 candidates to 528 candidates (-200.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New5280528
Fresh088
Picked011
Done011
Total52810538

Merged error: 1.0b

Counts
538 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

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:
11.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms
(pow (sin ky) 2.0)
16.0ms
(* (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)))

series134.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms
(pow (sin ky) 2.0)
48.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049332217
149332217

prune220.0ms

Filtered
87 candidates to 145 candidates (-66.7%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1387145
Fresh527
Picked011
Done112
Total14411155

Merged error: 0.9b

Counts
155 → 11

regimes806.0ms

Accuracy

67.7% (0.5b remaining)

Error of 2.9b against oracle of 2.5b and baseline of 3.9b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03144
13144

end0.0ms

sample6.7s

Algorithm
intervals
Results
3.9s3748×body1280valid
1.2s1992×body640valid
319.0ms743×body320valid
148.0ms1225×body80valid
83.0ms292×body160valid

Profiling

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