Details

Time bar (total: 9.1s)

sample120.0ms

Algorithm
intervals
Results
67.0ms96×body1280valid
25.0ms50×body640valid
7.0ms79×body80valid
6.0ms20×body320valid
2.0ms11×body160valid

simplify52.0ms

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: 11.5b

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))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.8b
(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:
47.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms
(pow (sin kx) 2.0)
2.0ms
(pow (sin ky) 2.0)
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series436.0ms

Counts
4 → 12
Calls
4 calls:
146.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
109.0ms
(pow (sin kx) 2.0)
103.0ms
(pow (sin ky) 2.0)
77.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify43.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0391990
11382928
25001927

prune425.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.3b

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (sin ky) 2.0)
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
41×sqrt-prod
40×add-cube-cbrt
30×associate-*r*
19×unpow-prod-down
16×distribute-lft-out
12×add-exp-log
11×add-cbrt-cube
8×pow1 associate-/r*
6×sqrt-div
4×associate-/r/ add-log-exp
3×pow-unpow flip3-+ associate-*l* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down pow-exp clear-num *-commutative sqr-pow
Counts
4 → 133
Calls
4 calls:
1.0ms
(pow (sin ky) 2.0)
48.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
19.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(pow (sin ky) 2.0)
139.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
134.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
73.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify57.0ms

Algorithm
egg-herbie
Counts
145 → 145
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04121572
118101426
250021423

prune447.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite63.0ms

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:
11.0ms
(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)))
15.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(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)))
75.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify103.0ms

Algorithm
egg-herbie
Counts
102 → 102
Iterations

Useful iterations: 3 (85.0ms)

IterNodesCost
02821291
18191231
234751224
350021219

prune486.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.3b

localize37.0ms

Local error

Found 4 expressions with local error:

3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite64.0ms

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)))
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)))
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series322.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
88.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify128.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
0118696
1301664
21019664
34120664
45001664

prune426.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 10.3b

regimes1.1s

Accuracy

0% (1.8b remaining)

Error of 12.9b against oracle of 11.2b and baseline of 12.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02234
12234

end0.0ms

sample3.7s

Algorithm
intervals
Results
2.0s2725×body1280valid
936.0ms1895×body640valid
210.0ms746×body320valid
206.0ms2253×body80valid
73.0ms381×body160valid