Details

Time bar (total: 9.7s)

sample205.0ms

Algorithm
intervals
Results
121.0ms117×body1280valid
54.0ms75×body640valid
8.0ms20×body320valid
4.0ms36×body80valid
2.0ms8×body160valid

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
0476616
1476616

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: 4.9b

Counts
2 → 2

localize15.0ms

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)
4.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite33.0ms

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:
18.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
2.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series104.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms
(pow (sin ky) 2.0)
19.0ms
(pow (sin kx) 2.0)
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
052511477

prune262.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10310113
Fresh011
Picked101
Done000
Total10411115

Merged error: 2.4b

Counts
115 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(/ (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)))))
4.6b
(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:
2.0ms
(pow (sin kx) 2.0)
12.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (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)))

series122.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin kx) 2.0)
42.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
43.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify69.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049432219
149432219

prune256.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1432145
Fresh3710
Picked011
Done000
Total14610156

Merged error: 2.4b

Counts
156 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.4b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
164×sqrt-prod
130×add-sqr-sqrt
123×times-frac
120×*-un-lft-identity
72×add-cube-cbrt
39×associate-*r* associate-*l*
24×unpow-prod-down distribute-lft-out
18×add-exp-log add-cbrt-cube
16×sqrt-div unswap-sqr
11×associate-/r*
8×pow1
6×associate-/r/
5×cbrt-undiv flip3-+ div-exp flip-+
4×prod-exp cbrt-unprod add-log-exp
3×div-inv associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 209
Calls
4 calls:
44.0ms
(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
11.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series128.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin th) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
41.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify61.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
051625280

prune520.0ms

Filtered
125 candidates to 221 candidates (-76.8%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2210221
Fresh088
Picked011
Done011
Total22110231

Merged error: 2.4b

Counts
231 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
4.6b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 48
Calls
4 calls:
2.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
8.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series74.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(cbrt (sin kx))
18.0ms
(cbrt (sin kx))
17.0ms
(cbrt (sin kx))
21.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify61.0ms

Algorithm
egg-herbie
Counts
60 → 60
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
04904609
14904609

prune105.0ms

Filtered
44 candidates to 60 candidates (-36.4%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New60060
Fresh077
Picked011
Done022
Total601070

Merged error: 2.4b

Counts
70 → 10

regimes952.0ms

Accuracy

68.4% (0.4b remaining)

Error of 3.1b against oracle of 2.7b and baseline of 3.9b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03853
13853

end0.0ms

sample6.3s

Algorithm
intervals
Results
4.0s3778×body1280valid
1.4s1992×body640valid
306.0ms687×body320valid
167.0ms1255×body80valid
77.0ms288×body160valid

Profiling

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