Details

Time bar (total: 15.5s)

sample112.0ms

Algorithm
intervals
Results
61.0ms83×body1280valid
23.0ms57×body640valid
7.0ms83×body80valid
6.0ms22×body320valid
2.0ms11×body160valid

simplify2.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01316
12316
23816
36716
413416
530716
689416
7323716
done500116

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

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 ky) 2.0)
0.2b
(pow (sin kx) 2.0)
4.7b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite47.0ms

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:
19.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.0ms
(pow (sin ky) 2.0)
2.0ms
(pow (sin kx) 2.0)
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series432.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
108.0ms
(pow (sin ky) 2.0)
107.0ms
(pow (sin kx) 2.0)
80.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.1s

Counts
129 → 129
Iterations

Useful iterations: 3 (395.0ms)

IterNodesCost
01781808
13421619
28721557
328501556
done50001556

prune454.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (sin kx) (sin ky))
0.1b
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
0.2b
(/ (sin ky) (hypot (sin kx) (sin ky)))

rewrite14.0ms

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 kx) (sin ky))
9.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
3.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))

series512.0ms

Counts
3 → 9
Calls
3 calls:
121.0ms
(hypot (sin kx) (sin ky))
225.0ms
(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
165.0ms
(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify1.3s

Counts
82 → 82
Iterations

Useful iterations: 3 (589.0ms)

IterNodesCost
01301126
12861107
2826987
32778984
done5000984

prune306.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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:
19.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
1.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
2.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

series908.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(* (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))) (cbrt (/ (sin ky) (hypot (sin kx) (sin ky)))))
222.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
217.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))
224.0ms
(cbrt (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify1.2s

Counts
164 → 164
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01713641
12913469
27803314
322383076
done50003069

prune890.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin ky))
0.6b
(cbrt (hypot (sin kx) (sin ky)))
0.6b
(cbrt (hypot (sin kx) (sin ky)))
0.6b
(cbrt (hypot (sin kx) (sin ky)))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt (sin ky))
0.0ms
(cbrt (hypot (sin kx) (sin ky)))
0.0ms
(cbrt (hypot (sin kx) (sin ky)))
1.0ms
(cbrt (hypot (sin kx) (sin ky)))

series557.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(cbrt (sin ky))
153.0ms
(cbrt (hypot (sin kx) (sin ky)))
154.0ms
(cbrt (hypot (sin kx) (sin ky)))
153.0ms
(cbrt (hypot (sin kx) (sin ky)))

simplify838.0ms

Counts
64 → 64
Iterations

Useful iterations: 4 (259.0ms)

IterNodesCost
064628
1126603
2287525
3648492
41966491
done5000491

prune244.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 7.1b

regimes768.0ms

Accuracy

0% (0.6b remaining)

Error of 9.6b against oracle of 9.0b and baseline of 9.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02282
12582
done2582

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.9s2684×body1280valid
727.0ms1759×body640valid
228.0ms821×body320valid
204.0ms2389×body80valid
61.0ms347×body160valid