Details

Time bar (total: 9.2s)

sample157.0ms

Algorithm
intervals
Results
99.0ms119×body1280valid
31.0ms67×body640valid
7.0ms23×body320valid
4.0ms36×body80valid
2.0ms11×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13910
26710
315310
443910
5181710
6500110

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: 2.3b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.2b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×sqrt-div sqr-pow
2×pow-to-exp flip3-+ associate-/r/ flip-+
1×frac-2neg pow1/2 clear-num hypot-def div-inv
Counts
4 → 13
Calls
4 calls:
5.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
2.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
4.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series406.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
99.0ms
(pow (sin kx) 2.0)
102.0ms
(pow (sin ky) 2.0)
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
25 → 25
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0170171
1526162
21945161
35001161

prune99.0ms

Filtered
25 candidates to 19 candidates (76.0%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New20525
Fresh000
Picked101
Done000
Total21526

Merged error: 0.1b

Counts
26 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.1b
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
0.2b
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*l/
2×frac-2neg clear-num div-inv
1×hypot-udef associate-*l* *-commutative
Counts
3 → 9
Calls
3 calls:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
4.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
3.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

series950.0ms

Counts
3 → 9
Calls
3 calls:
248.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
329.0ms
(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))
373.0ms
(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

simplify40.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0124126
1405120
21528119
35001119

prune75.0ms

Filtered
18 candidates to 14 candidates (77.8%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New14418
Fresh224
Picked101
Done000
Total17623

Merged error: 0.0b

Counts
23 → 6

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.2b
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.3b
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×associate-*r/ clear-num
2×frac-2neg div-inv
1×hypot-udef associate-*r* un-div-inv *-commutative
Counts
3 → 10
Calls
3 calls:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
3.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
7.0ms
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series920.0ms

Counts
3 → 9
Calls
3 calls:
240.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
324.0ms
(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
355.0ms
(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify44.0ms

Algorithm
egg-herbie
Counts
19 → 19
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0120117
1372111
21348110
35001110

prune77.0ms

Filtered
19 candidates to 14 candidates (73.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New17219
Fresh055
Picked101
Done000
Total18725

Merged error: 0.0b

Counts
25 → 7

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.2b
(/ (sin ky) (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin th)))
0.3b
(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin th))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
3×frac-2neg clear-num associate-/r/ div-inv
1×hypot-udef associate-/r*
Counts
3 → 11
Calls
3 calls:
1.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
4.0ms
(/ (sin ky) (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin th)))
2.0ms
(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin th))

series888.0ms

Counts
3 → 9
Calls
3 calls:
251.0ms
(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
340.0ms
(/ (sin ky) (/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin th)))
297.0ms
(/ (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))) (sin th))

simplify43.0ms

Algorithm
egg-herbie
Counts
20 → 20
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0143170
1435156
21551153
35002153

prune56.0ms

Filtered
20 candidates to 14 candidates (70.0%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New19120
Fresh066
Picked011
Done000
Total19827

Merged error: 0.0b

Counts
27 → 8

regimes328.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01411

end0.0ms

sample4.9s

Algorithm
intervals
Results
3.1s3766×body1280valid
1.1s1973×body640valid
232.0ms699×body320valid
132.0ms1286×body80valid
58.0ms276×body160valid