Details

Time bar (total: 29.5s)

sample358.0ms

Algorithm
intervals
Results
136.0ms84×body1280valid
47.0ms62×body640valid
17.0ms29×body320valid
15.0ms71×body80valid
4.0ms10×body160valid

simplify4.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
01316
12316
23516
36416
413616
531116
6101916
7422316
done500116

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize24.0ms

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)
2.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite95.0ms

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:
46.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
37.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series637.0ms

Counts
4 → 12
Calls
4 calls:
178.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
157.0ms
(pow (sin kx) 2.0)
157.0ms
(pow (sin ky) 2.0)
145.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts
112 → 112
Iterations

Useful iterations: 2 (273.0ms)

IterNodesCost
01701738
13281556
27941503
324191503
done50001503

prune661.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin kx) 2.0)
0.3b
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(pow (sin ky) 2.0)
2.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite214.0ms

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:
7.0ms
(pow (sin kx) 2.0)
152.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
8.0ms
(pow (sin ky) 2.0)
39.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(pow (sin kx) 2.0)
184.0ms
(* (sin ky) (/ 1 (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
157.0ms
(pow (sin ky) 2.0)
120.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.7s

Counts
118 → 118
Iterations

Useful iterations: 2 (251.0ms)

IterNodesCost
01981690
14331384
210901284
332401284
done50011284

prune523.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
2.4b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite56.0ms

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:
3.0ms
(cbrt (sin kx))
4.0ms
(cbrt (sin kx))
13.0ms
(cbrt (sin kx))
34.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series581.0ms

Counts
4 → 12
Calls
4 calls:
185.0ms
(cbrt (sin kx))
125.0ms
(cbrt (sin kx))
151.0ms
(cbrt (sin kx))
120.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify1.7s

Counts
60 → 60
Iterations

Useful iterations: 3 (493.0ms)

IterNodesCost
081818
1187744
2478620
31767609
done5001609

prune494.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.9b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.4b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite168.0ms

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:
35.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
32.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
34.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
59.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series587.0ms

Counts
4 → 12
Calls
4 calls:
231.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
116.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
114.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
126.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.5s

Counts
102 → 102
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01602119
12821894
26361807
317031797
done50011791

prune699.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.9b

regimes1.6s

Accuracy

0% (1.6b remaining)

Error of 12.9b against oracle of 11.3b and baseline of 12.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01727
12027
done2027

end0.0ms

sample9.4s

Algorithm
intervals
Results
5.2s2639×body1280valid
2.4s1890×body640valid
621.0ms834×body320valid
495.0ms2351×body80valid
132.0ms286×body160valid