Details

Time bar (total: 10.4s)

sample178.0ms

Algorithm
intervals
Results
116.0ms118×body1280valid
32.0ms58×body640valid
7.0ms20×body320valid
5.0ms46×body80valid
4.0ms14×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.5b

Counts
2 → 1

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 kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite39.0ms

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

series464.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
108.0ms
(pow (sin kx) 2.0)
114.0ms
(pow (sin ky) 2.0)
78.0ms
(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
0391990
11382928
25001927

prune386.0ms

Filtered
113 candidates to 78 candidates (69.0%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10211113
Fresh000
Picked101
Done000
Total10311114

Merged error: 2.4b

Counts
114 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(pow (sin ky) 2.0)
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite46.0ms

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:
18.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.0ms
(pow (sin ky) 2.0)
12.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series488.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
109.0ms
(pow (sin ky) 2.0)
144.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
83.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify64.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04121572
118101426
250011423

prune384.0ms

Filtered
145 candidates to 86 candidates (59.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1423145
Fresh4610
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)))))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite96.0ms

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:
49.0ms
(* (/ (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))))))
13.0ms
(/ (sin ky) (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)))
11.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series490.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* (/ (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))))))
164.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
84.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify92.0ms

Algorithm
egg-herbie
Counts
221 → 221
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
06814176
128773811
250013715

prune631.0ms

Filtered
221 candidates to 127 candidates (57.5%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New2210221
Fresh088
Picked011
Done011
Total22110231

Merged error: 2.4b

Counts
231 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 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)))))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite53.0ms

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)
28.0ms
(* (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)))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series360.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(pow (sin ky) 2.0)
82.0ms
(* (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
85.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03121456
111941355
250011324

prune362.0ms

Filtered
154 candidates to 74 candidates (48.1%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1540154
Fresh077
Picked011
Done022
Total15410164

Merged error: 2.4b

Counts
164 → 10

regimes375.0ms

Accuracy

0% (1.4b remaining)

Error of 4.2b against oracle of 2.8b and baseline of 4.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

sample5.6s

Algorithm
intervals
Results
3.6s3756×body1280valid
1.3s1987×body640valid
285.0ms718×body320valid
135.0ms1238×body80valid
73.0ms301×body160valid

Profiling

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