Details

Time bar (total: 26.3s)

sample8.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results
121.0ms114×body1280valid
52.0ms74×body640valid
10.0ms24×body320valid
4.0ms35×body80valid
2.0ms9×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.8b

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))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite32.0ms

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:
14.0ms
(* (/ (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)
6.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series102.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
17.0ms
(pow (sin kx) 2.0)
18.0ms
(pow (sin ky) 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

prune270.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New10310113
Fresh000
Picked101
Done000
Total10410114

Merged error: 2.2b

Counts
114 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))
13.4b
(cbrt (pow (sin ky) 2.0))
13.4b
(cbrt (pow (sin ky) 2.0))
13.4b
(cbrt (pow (sin ky) 2.0))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×add-cube-cbrt *-un-lft-identity
9×unpow-prod-down
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 60
Calls
4 calls:
4.0ms
(sqrt (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))
2.0ms
(cbrt (pow (sin ky) 2.0))
2.0ms
(cbrt (pow (sin ky) 2.0))
2.0ms
(cbrt (pow (sin ky) 2.0))

series130.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (* (* (cbrt (pow (sin ky) 2.0)) (cbrt (pow (sin ky) 2.0))) (cbrt (pow (sin ky) 2.0)))))
37.0ms
(cbrt (pow (sin ky) 2.0))
35.0ms
(cbrt (pow (sin ky) 2.0))
38.0ms
(cbrt (pow (sin ky) 2.0))

simplify75.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0215721
1602679
22161649
35001643

prune241.0ms

Filtered
55 candidates to 72 candidates (-30.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New72072
Fresh099
Picked011
Done000
Total721082

Merged error: 2.2b

Counts
82 → 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)))))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite43.0ms

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:
2.0ms
(pow (sin ky) 2.0)
21.0ms
(* (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)))
8.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series75.0ms

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

simplify56.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
03301472
112661371
250021333

prune293.0ms

Filtered
74 candidates to 154 candidates (-108.1%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1540154
Fresh088
Picked011
Done011
Total15410164

Merged error: 2.2b

Counts
164 → 10

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.8b
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
87×*-un-lft-identity
66×times-frac
53×add-sqr-sqrt
51×add-cube-cbrt
45×add-exp-log
39×associate-*l*
27×add-cbrt-cube
20×prod-exp
18×unpow-prod-down distribute-lft-out
12×sqrt-div
11×pow1 div-exp associate-/r*
10×cbrt-unprod
6×cbrt-undiv
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×rec-exp 1-exp pow-prod-down associate-*l/ associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 div-inv
1×frac-times frac-2neg associate-*r/ associate-*r* clear-num *-commutative
Counts
4 → 166
Calls
4 calls:
11.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
28.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th)))
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:
43.0ms
(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
46.0ms
(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (* (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (sin th)))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
21.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify82.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
05923073
130092574
250022305

prune397.0ms

Filtered
104 candidates to 178 candidates (-71.2%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1762178
Fresh257
Picked011
Done022
Total17810188

Merged error: 2.1b

Counts
188 → 10

regimes808.0ms

Accuracy

0% (1.2b remaining)

Error of 4.4b against oracle of 3.1b and baseline of 4.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01919
11919

end0.0ms

sample14.9s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 70.898438%

Results
4.0s3673×body1280valid
1.4s2081×body640valid
313.0ms691×body320valid
166.0ms1290×body80valid
74.0ms265×body160valid

Profiling

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