Details

Time bar (total: 8.5s)

sample160.0ms

Algorithm
intervals
Results
95.0ms120×body1280valid
35.0ms62×body640valid
9.0ms26×body320valid
4.0ms38×body80valid
2.0ms10×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5178510
6500210

prune4.0ms

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: 3.2b

Counts
2 → 1

localize17.0ms

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)
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
4×sqrt-div
3×associate-*l* associate-*l/
2×pow-to-exp flip3-+ associate-/r/ flip-+ sqr-pow
1×frac-2neg pow1/2 clear-num *-commutative div-inv
Counts
4 → 14
Calls
4 calls:
7.0ms
(* (/ (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)
3.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
105.0ms
(pow (sin kx) 2.0)
107.0ms
(pow (sin ky) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify70.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0174169
1553169
22238169
35002169

prune115.0ms

Filtered
26 candidates to 20 candidates (76.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New19726
Fresh000
Picked011
Done000
Total19827

Merged error: 1.9b

Counts
27 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
5×associate-/r/
4×sqrt-div
2×pow-to-exp frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l/ sqr-pow
1×pow1/2 associate-/r*
Counts
4 → 16
Calls
4 calls:
6.0ms
(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
2.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
3.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series449.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(/ (sin th) (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
108.0ms
(pow (sin kx) 2.0)
104.0ms
(pow (sin ky) 2.0)
79.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify69.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 3 (65.0ms)

IterNodesCost
0175205
1518205
22028205
35001204

prune124.0ms

Filtered
28 candidates to 20 candidates (71.4%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New25328
Fresh066
Picked011
Done011
Total251136

Merged error: 1.9b

Counts
36 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
0.4b
(/ 1 (/ (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)) (sin th)))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
9×associate-/r/
8×associate-/l/
5×clear-num
4×sqrt-div
3×frac-2neg div-inv
2×pow-to-exp flip3-+ flip-+ remove-double-div sqr-pow
1×pow1/2 associate-/r* associate-/l* inv-pow
Counts
4 → 23
Calls
4 calls:
5.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
7.0ms
(/ 1 (/ (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)) (sin th)))
3.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series453.0ms

Counts
4 → 12
Calls
4 calls:
110.0ms
(pow (sin kx) 2.0)
106.0ms
(pow (sin ky) 2.0)
163.0ms
(/ 1 (/ (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)) (sin th)))
73.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify75.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 3 (71.0ms)

IterNodesCost
0182230
1566229
22337229
35001226

prune138.0ms

Filtered
35 candidates to 23 candidates (65.7%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New33235
Fresh178
Picked101
Done022
Total351146

Merged error: 1.9b

Counts
46 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
0.3b
(/ (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th)))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
7×associate-/r/ div-inv
6×sqrt-div
3×frac-2neg flip3-+ times-frac clear-num flip-+ associate-/l/ associate-/l*
2×pow-to-exp sqr-pow
1×pow1/2 associate-/r*
Counts
4 → 23
Calls
4 calls:
2.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
7.0ms
(/ (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th)))
3.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow (sin kx) 2.0)
106.0ms
(pow (sin ky) 2.0)
156.0ms
(/ (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin th)))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify138.0ms

Algorithm
egg-herbie
Counts
35 → 35
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0228318
1800307
23681307
35001307

prune101.0ms

Filtered
35 candidates to 20 candidates (57.1%)
Pruning

11 alts after pruning (8 fresh and 3 done)

PrunedKeptTotal
New35035
Fresh088
Picked011
Done022
Total351146

Merged error: 1.9b

Counts
46 → 11

regimes532.0ms

Accuracy

0% (1.4b remaining)

Error of 3.8b against oracle of 2.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01510
11510

end0.0ms

sample5.0s

Algorithm
intervals
Results
3.3s3781×body1280valid
1.1s2014×body640valid
234.0ms686×body320valid
126.0ms1252×body80valid
60.0ms267×body160valid