Details

Time bar (total: 9.3s)

sample185.0ms

Algorithm
intervals
Results
110.0ms113×body1280valid
40.0ms60×body640valid
11.0ms29×body320valid
4.0ms39×body80valid
4.0ms15×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune4.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 2.9b

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)))

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:
20.0ms
(* (/ (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)))

series103.0ms

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 kx) 2.0)
18.0ms
(pow (sin ky) 2.0)
19.0ms
(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

prune256.0ms

Filtered
113 candidates to 78 candidates (31.0%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1049113
Fresh000
Picked011
Done000
Total10410114

Merged error: 2.0b

Counts
114 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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:
18.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
16.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms
(pow (sin ky) 2.0)
7.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series124.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin ky) (* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th)))
41.0ms
(* (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
18.0ms
(pow (sin ky) 2.0)
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify52.0ms

Algorithm
egg-herbie
Counts
123 → 123
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
04431278
118401119
250011095

prune234.0ms

Filtered
123 candidates to 80 candidates (35.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1212123
Fresh268
Picked011
Done011
Total12310133

Merged error: 2.0b

Counts
133 → 10

localize20.0ms

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)))

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 ky) 2.0)
23.0ms
(* (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)))

series76.0ms

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

simplify55.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
03301472
112661371
250021333

prune289.0ms

Filtered
154 candidates to 74 candidates (51.9%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New1531154
Fresh077
Picked011
Done022
Total15311164

Merged error: 2.0b

Counts
164 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
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)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite34.0ms

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:
10.0ms
(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)))
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)))

series109.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
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)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify124.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (110.0ms)

IterNodesCost
03081314
19091257
240971241
350031236

prune338.0ms

Filtered
102 candidates to 68 candidates (33.3%)
Pruning

11 alts after pruning (7 fresh and 4 done)

PrunedKeptTotal
New1011102
Fresh167
Picked011
Done033
Total10211113

Merged error: 2.0b

Counts
113 → 11

regimes924.0ms

Accuracy

0% (1.2b remaining)

Error of 3.8b against oracle of 2.6b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.8s3748×body1280valid
1.3s2062×body640valid
290.0ms1217×body80valid
281.0ms680×body320valid
84.0ms293×body160valid

Profiling

Loading profile data...