Details

Time bar (total: 11.6s)

analyze1.4s

Algorithm
search

sample196.0ms

Algorithm
intervals
Results
123.0ms116×body1280valid
42.0ms66×body640valid
12.0ms28×body320valid
5.0ms39×body80valid
2.0ms7×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune5.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.6b

Counts
2 → 1

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)
0.3b
(pow (sin kx) 2.0)
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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:
19.0ms
(* (/ (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)))

series105.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms
(pow (sin ky) 2.0)
18.0ms
(pow (sin kx) 2.0)
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify44.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04251022
11522960
25001946

prune287.0ms

Filtered
78 candidates to 113 candidates (-44.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10112113
Fresh000
Picked101
Done000
Total10212114

Merged error: 2.2b

Counts
114 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
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))
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
37×add-sqr-sqrt
33×associate-*l*
29×add-exp-log
28×times-frac
24×add-cube-cbrt
22×sqrt-prod
18×add-cbrt-cube
13×pow1 prod-exp
11×unpow-prod-down
8×distribute-lft-out
7×cbrt-unprod
5×unswap-sqr
4×sqrt-div div-exp associate-*r* pow-prod-down add-log-exp
3×pow-unpow
2×cbrt-undiv rec-exp flip3-+ 1-exp associate-*l/ associate-/r/ *-commutative flip-+
1×pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow1/2 associate-*r/ pow-exp div-inv sqr-pow
Counts
4 → 111
Calls
4 calls:
2.0ms
(pow (sin kx) 2.0)
15.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
18.0ms
(* (/ 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)))

series127.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin kx) 2.0)
48.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
42.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify50.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04431278
117811120
250011095

prune258.0ms

Filtered
80 candidates to 123 candidates (-53.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1221123
Fresh11011
Picked011
Done000
Total12312135

Merged error: 2.2b

Counts
135 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(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)))))
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite41.0ms

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)
10.0ms
(/ (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)))

series128.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(pow (sin kx) 2.0)
42.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
45.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
21.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
04301588
117551442
250011432

prune275.0ms

Filtered
86 candidates to 145 candidates (-68.6%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1441145
Fresh1910
Picked011
Done011
Total14512157

Merged error: 2.2b

Counts
157 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.5b
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

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 kx) 2.0)
22.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
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)))

series79.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(pow (sin kx) 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)))))
23.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify54.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03271472
112561371
250011333

prune262.0ms

Filtered
75 candidates to 154 candidates (-105.3%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New1540154
Fresh099
Picked011
Done022
Total15412166

Merged error: 2.2b

Counts
166 → 12

regimes695.0ms

Accuracy

0% (1.3b remaining)

Error of 3.7b against oracle of 2.4b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

analyze1.2s

Algorithm
search

sample6.1s

Algorithm
intervals
Results
4.0s3765×body1280valid
1.3s1992×body640valid
319.0ms707×body320valid
157.0ms1260×body80valid
87.0ms276×body160valid

Profiling

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