Details

Time bar (total: 9.4s)

sample129.0ms

Algorithm
intervals
Results
66.0ms77×body1280valid
31.0ms64×body640valid
8.0ms80×body80valid
7.0ms22×body320valid
3.0ms13×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02310
13510
26310
313710
441710
5179810
6500210

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.6b

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 ky) 2.0)
0.3b
(pow (sin kx) 2.0)
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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:
46.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
1.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
20.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
143.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
108.0ms
(pow (sin ky) 2.0)
103.0ms
(pow (sin kx) 2.0)
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify42.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0391990
11382928
25001927

prune410.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite65.0ms

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:
14.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series385.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
72.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify98.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (86.0ms)

IterNodesCost
02821291
18191231
234751224
350021219

prune477.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin ky))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
15×sqrt-prod
11×add-sqr-sqrt
8×add-cube-cbrt
7×pow1
6×unpow-prod-down sqrt-div distribute-lft-out
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
1×pow1/3
Counts
4 → 62
Calls
4 calls:
1.0ms
(cbrt (sin ky))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series324.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(cbrt (sin ky))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
74.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify59.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0171583
1424554
21478552
35002551

prune427.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 8.4b

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity
20×sqrt-prod
12×add-sqr-sqrt
8×pow1 add-cube-cbrt unpow-prod-down sqrt-div distribute-lft-out
4×add-exp-log rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ add-log-exp
Counts
4 → 68
Calls
4 calls:
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify127.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0118696
1301664
21019664
34120664
45001664

prune352.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 8.4b

regimes1.2s

Accuracy

0% (1.7b remaining)

Error of 13.1b against oracle of 11.4b and baseline of 13.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02354
12354

end0.0ms

sample4.2s

Algorithm
intervals
Results
2.3s2768×body1280valid
914.0ms1791×body640valid
398.0ms2279×body80valid
272.0ms789×body320valid
82.0ms373×body160valid