Details

Time bar (total: 16.4s)

sample118.0ms

Algorithm
intervals
Results
64.0ms90×body1280valid
28.0ms66×body640valid
6.0ms25×body320valid
5.0ms62×body80valid
2.0ms13×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01316
12316
23416
36316
412616
529816
699416
7400416
done500016

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.7b

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))))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
4.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
27×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
16×unpow-prod-down
10×distribute-lft-out
8×add-exp-log associate-/r*
7×pow1
6×pow-unpow add-cbrt-cube
4×sqrt-div add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 100
Calls
4 calls:
23.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms
(pow (sin kx) 2.0)
1.0ms
(pow (sin ky) 2.0)
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series414.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
102.0ms
(pow (sin kx) 2.0)
102.0ms
(pow (sin ky) 2.0)
78.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts
112 → 112
Iterations

Useful iterations: 2 (120.0ms)

IterNodesCost
01701738
13301550
29341503
344551503
done50001503

prune395.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
4.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
150×*-un-lft-identity
99×add-sqr-sqrt
98×add-cube-cbrt
65×sqrt-prod
32×unpow-prod-down
28×associate-/r*
26×distribute-lft-out
17×add-exp-log
9×add-cbrt-cube
8×pow1
7×div-exp
6×pow-unpow
5×div-inv
4×add-log-exp
3×cbrt-undiv associate-/l*
2×pow-to-exp rec-exp pow-pow sqrt-div 1-exp pow-exp sqr-pow
1×rem-sqrt-square pow-flip frac-2neg sqrt-pow1 flip3-+ pow1/2 clear-num associate-/r/ flip-+ inv-pow
Counts
4 → 187
Calls
4 calls:
26.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
1.0ms
(pow (sin kx) 2.0)
1.0ms
(pow (sin ky) 2.0)
16.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
120.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
104.0ms
(pow (sin kx) 2.0)
106.0ms
(pow (sin ky) 2.0)
125.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.2s

Counts
199 → 199
Iterations

Useful iterations: 2 (357.0ms)

IterNodesCost
02884423
16423676
218543406
done50003406

prune414.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
4.1b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log add-cbrt-cube add-log-exp
3×pow1/3 sqrt-prod
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 48
Calls
4 calls:
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
1.0ms
(cbrt (sin kx))
13.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series364.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (sin kx))
95.0ms
(cbrt (sin kx))
95.0ms
(cbrt (sin kx))
76.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify710.0ms

Counts
60 → 60
Iterations

Useful iterations: 3 (186.0ms)

IterNodesCost
081818
1187744
2488620
31730609
done5000609

prune329.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.1b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite64.0ms

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)))
18.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series394.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
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)))
76.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.3s

Counts
102 → 102
Iterations

Useful iterations: 3 (414.0ms)

IterNodesCost
01602119
12841894
27541807
328861797
done50011797

prune400.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 10.3b

regimes1.1s

Accuracy

0% (1.6b remaining)

Error of 12.5b against oracle of 10.9b and baseline of 12.5b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02260
12660
done2660

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s2763×body1280valid
785.0ms1892×body640valid
201.0ms757×body320valid
196.0ms2267×body80valid
60.0ms321×body160valid