Details

Time bar (total: 28.8s)

sample565.0ms

Algorithm
intervals
Results
183.0ms88×body1280valid
128.0ms12×body160valid
88.0ms61×body640valid
12.0ms76×body80valid
11.0ms19×body320valid

simplify5.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01316
12316
23516
36416
413616
531116
6101916
7422316
done500116

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize19.0ms

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)
3.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite93.0ms

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:
45.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
31.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.1s

Counts
4 → 12
Calls
4 calls:
637.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
159.0ms
(pow (sin kx) 2.0)
143.0ms
(pow (sin ky) 2.0)
118.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts
112 → 112
Iterations

Useful iterations: 2 (192.0ms)

IterNodesCost
01701738
13281556
27941503
324191503
done50001503

prune627.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
0.3b
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
38×add-sqr-sqrt
30×associate-*r*
28×times-frac
25×add-cube-cbrt
22×sqrt-prod
15×add-exp-log
14×unpow-prod-down
9×pow1 add-cbrt-cube
8×distribute-lft-out
6×pow-unpow
5×unswap-sqr
4×sqrt-div prod-exp add-log-exp
3×associate-*l*
2×pow-to-exp pow-pow flip3-+ div-exp pow-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative div-inv
Counts
4 → 106
Calls
4 calls:
4.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
145.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
42.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series652.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(pow (sin kx) 2.0)
158.0ms
(pow (sin ky) 2.0)
210.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
108.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.8s

Counts
118 → 118
Iterations

Useful iterations: 2 (299.0ms)

IterNodesCost
01981690
14331384
210951284
332701284
done50021284

prune621.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 11.2b

localize18.0ms

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)
3.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite123.0ms

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:
49.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
5.0ms
(pow (sin kx) 2.0)
7.0ms
(pow (sin ky) 2.0)
51.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series664.0ms

Counts
4 → 12
Calls
4 calls:
177.0ms
(/ 1 (/ (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))) (sin ky)))
183.0ms
(pow (sin kx) 2.0)
172.0ms
(pow (sin ky) 2.0)
131.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.9s

Counts
199 → 199
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
02884423
16013676
212423406
335553358
done50003358

prune561.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 11.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
0.2b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
3.5b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite236.0ms

Algorithm
rewrite-expression-head
Rules
1005×times-frac
608×*-un-lft-identity
437×add-sqr-sqrt
436×add-cube-cbrt
215×sqrt-prod
92×unpow-prod-down
86×distribute-lft-out
46×add-exp-log div-inv
32×div-exp
30×sqrt-div associate-/l*
29×associate-/r/
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv rec-exp 1-exp
7×pow1
6×pow-unpow
4×add-log-exp
2×pow-to-exp pow-pow pow-exp sqr-pow
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 516
Calls
4 calls:
104.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
8.0ms
(pow (sin kx) 2.0)
7.0ms
(pow (sin ky) 2.0)
56.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
173.0ms
(/ (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (/ 1 (sin ky)))
137.0ms
(pow (sin kx) 2.0)
142.0ms
(pow (sin ky) 2.0)
110.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.3s

Counts
528 → 528
Iterations

Useful iterations: done (2.3s)

IterNodesCost
068617925
1177013716
2283612634
done500112466

prune824.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.2b

regimes1.2s

Accuracy

0% (1.3b remaining)

Error of 12.2b against oracle of 10.9b and baseline of 12.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
01518
12016
done2016

end0.0ms

sample5.5s

Algorithm
intervals
Results
3.1s2761×body1280valid
1.2s1851×body640valid
313.0ms2326×body80valid
308.0ms734×body320valid
89.0ms328×body160valid