Details

Time bar (total: 10.1s)

sample183.0ms

Algorithm
intervals
Results
109.0ms118×body1280valid
35.0ms61×body640valid
18.0ms21×body320valid
5.0ms43×body80valid
3.0ms13×body160valid

simplify52.0ms

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: 4.7b

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)
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite35.0ms

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:
21.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
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)))

series437.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
105.0ms
(pow (sin kx) 2.0)
102.0ms
(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 (33.0ms)

IterNodesCost
0391990
11382928
25001927

prune378.0ms

Filtered
113 candidates to 78 candidates (69.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New10112113
Fresh000
Picked101
Done000
Total10212114

Merged error: 3.0b

Counts
114 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b
(pow (sin ky) 2.0)
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite45.0ms

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)
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)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
104.0ms
(pow (sin ky) 2.0)
143.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
70.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify65.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04121572
118101426
250011423

prune363.0ms

Filtered
145 candidates to 85 candidates (58.6%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1450145
Fresh01111
Picked011
Done000
Total14512157

Merged error: 3.0b

Counts
157 → 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)))))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite36.0ms

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:
9.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series388.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
72.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify98.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
02821291
18191231
234611223
350021218

prune376.0ms

Filtered
102 candidates to 68 candidates (66.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1020102
Fresh01010
Picked011
Done011
Total10212114

Merged error: 3.0b

Counts
114 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
1.1b
(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.5b
(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.3b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
16×log-prod
15×sqrt-prod
13×add-sqr-sqrt
12×add-cube-cbrt
10×pow1
9×unpow-prod-down
8×exp-sum
6×add-exp-log exp-prod sqrt-div log-pow distribute-lft-out
4×log-div add-cbrt-cube add-log-exp
3×pow-unpow sqrt-pow1 flip3-+ pow1/2 flip-+
2×exp-diff
1×pow-to-exp rem-sqrt-square pow-pow rem-log-exp pow-exp rem-exp-log sqr-pow
Counts
4 → 79
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
7.0ms
(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
9.0ms
(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(pow (sin ky) 2.0)
92.0ms
(log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
76.0ms
(exp (log (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 3 (66.0ms)

IterNodesCost
0250773
1692728
22182712
35001706

prune253.0ms

Filtered
91 candidates to 57 candidates (62.6%)
Pruning

13 alts after pruning (10 fresh and 3 done)

PrunedKeptTotal
New90191
Fresh099
Picked011
Done022
Total9013103

Merged error: 3.0b

Counts
103 → 13

regimes668.0ms

Accuracy

67.2% (0.5b remaining)

Error of 3.2b against oracle of 2.7b and baseline of 4.2b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03729
13729

end0.0ms

sample5.7s

Algorithm
intervals
Results
3.6s3750×body1280valid
1.2s1976×body640valid
293.0ms1275×body80valid
291.0ms714×body320valid
69.0ms285×body160valid

Profiling

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