Details

Time bar (total: 33.1s)

sample480.0ms

Algorithm
intervals
Results
277.0ms84×body1280valid
91.0ms62×body640valid
18.0ms29×body320valid
15.0ms71×body80valid
4.0ms10×body160valid

simplify5.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
01316
12316
23916
36816
415216
533316
6104916
7430516
done500116

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize21.0ms

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)))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
46×*-un-lft-identity
39×add-sqr-sqrt
26×add-cube-cbrt
25×sqrt-prod
24×times-frac
22×unpow-prod-down
10×distribute-lft-out
9×hypot-def
8×add-exp-log associate-/r* sqr-pow
7×pow1
6×pow-unpow add-cbrt-cube
4×expm1-log1p-u sqrt-div log1p-expm1-u add-log-exp
3×associate-/l*
2×pow-to-exp pow-pow flip3-+ pow-exp associate-/r/ flip-+
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
4 → 117
Calls
4 calls:
65.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
5.0ms
(pow (sin kx) 2.0)
4.0ms
(pow (sin ky) 2.0)
44.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series700.0ms

Counts
4 → 12
Calls
4 calls:
221.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
189.0ms
(pow (sin kx) 2.0)
150.0ms
(pow (sin ky) 2.0)
140.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts
129 → 129
Iterations

Useful iterations: 3 (740.0ms)

IterNodesCost
01781808
13401625
28501557
326401556
done50001556

prune735.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.8b

localize16.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (sin ky) (sin kx))
0.2b
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*l*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*r* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
0.0ms
(hypot (sin ky) (sin kx))
22.0ms
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
10.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))

series765.0ms

Counts
3 → 9
Calls
3 calls:
212.0ms
(hypot (sin ky) (sin kx))
331.0ms
(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
222.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.1s

Counts
82 → 82
Iterations

Useful iterations: 3 (753.0ms)

IterNodesCost
01301126
12841106
2790987
32333984
done5000984

prune534.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize29.0ms

Local error

Found 3 expressions with local error:

0.1b
(hypot (sin ky) (sin kx))
0.2b
(/ (sin th) (hypot (sin ky) (sin kx)))
0.2b
(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity times-frac
13×associate-*r*
10×add-exp-log add-cbrt-cube
5×pow1
3×expm1-log1p-u associate-*l* associate-/r* log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef frac-2neg associate-*r/ pow-prod-down clear-num *-commutative
Counts
3 → 73
Calls
3 calls:
1.0ms
(hypot (sin ky) (sin kx))
19.0ms
(/ (sin th) (hypot (sin ky) (sin kx)))
47.0ms
(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series822.0ms

Counts
3 → 9
Calls
3 calls:
216.0ms
(hypot (sin ky) (sin kx))
279.0ms
(/ (sin th) (hypot (sin ky) (sin kx)))
327.0ms
(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify2.3s

Counts
82 → 82
Iterations

Useful iterations: 3 (853.0ms)

IterNodesCost
01211123
12521091
2782976
32471975
done5000975

prune489.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
103×cbrt-prod
81×add-sqr-sqrt
69×times-frac
57×add-cube-cbrt *-un-lft-identity
16×swap-sqr associate-*r* associate-*l*
11×pow1
9×pow1/3 unswap-sqr
7×cbrt-div div-inv
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp *-commutative cbrt-unprod
Counts
4 → 152
Calls
4 calls:
34.0ms
(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
3.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
9.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.3s

Counts
4 → 12
Calls
4 calls:
358.0ms
(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
352.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
295.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
295.0ms
(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify3.4s

Counts
164 → 164
Iterations

Useful iterations: done (3.4s)

IterNodesCost
01713641
12903469
27553314
315503076
440463045
done50002977

prune1.1s

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.8b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0911
11011
done1011

end0.0ms

sample9.3s

Algorithm
intervals
Results
4.4s2639×body1280valid
2.8s1890×body640valid
982.0ms2351×body80valid
512.0ms834×body320valid
110.0ms286×body160valid