Details

Time bar (total: 25.7s)

sample341.0ms

Algorithm
intervals
Results
157.0ms87×body1280valid
40.0ms67×body640valid
10.0ms72×body80valid
7.0ms13×body160valid
7.0ms17×body320valid

simplify1.0s

Counts
1 → 1
Iterations
IterNodes
done5000
5632
4140
364
235
123
013

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.9b

localize53.0ms

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)
0.2b
(pow (sin ky) 2.0)
3.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite74.0ms

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×associate-/r* add-exp-log
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 clear-num frac-2neg sqrt-pow1 pow1/2 div-exp div-inv
Counts
4 → 100
Calls
4 calls:
37.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
24.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series683.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
131.0ms
(pow (sin kx) 2.0)
202.0ms
(pow (sin ky) 2.0)
134.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify820.0ms

Counts
112 → 112
Iterations
IterNodes
done5001
21591
1382
0170

prune914.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.8b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
0.2b
(pow (sin ky) 2)
0.3b
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
3.8b
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

rewrite161.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
49×add-sqr-sqrt times-frac
45×sqrt-prod
36×add-cube-cbrt
24×associate-*l*
23×unpow-prod-down
20×distribute-lft-out
11×add-exp-log
10×pow1
8×add-cbrt-cube
6×associate-/r/
5×associate-/r*
4×add-log-exp unswap-sqr
3×rem-sqrt-square pow-unpow sqrt-pow1 flip3-+ associate-*r* flip-+ div-inv associate-/l*
2×sqrt-div div-exp pow-flip inv-pow
1×pow-to-exp cbrt-undiv rec-exp clear-num pow-pow frac-2neg pow1/2 1-exp pow-prod-down associate-*l/ pow-exp prod-exp *-commutative cbrt-unprod unpow2 sqr-pow
Counts
4 → 138
Calls
4 calls:
36.0ms
(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
3.0ms
(pow (sin ky) 2)
77.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
34.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

series487.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))
27.0ms
(pow (sin ky) 2)
197.0ms
(* (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2)))) (sin ky))
147.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

simplify1.6s

Counts
150 → 150
Iterations
IterNodes
done5001
21907
1431
0191

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.7b

localize54.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
3.8b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×add-cbrt-cube add-exp-log 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:
2.0ms
(cbrt (sin kx))
2.0ms
(cbrt (sin kx))
2.0ms
(cbrt (sin kx))
33.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series532.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(cbrt (sin kx))
132.0ms
(cbrt (sin kx))
154.0ms
(cbrt (sin kx))
123.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify1.5s

Counts
60 → 60
Iterations
IterNodes
done5002
32801
2573
1191
081

prune707.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 9.7b

localize140.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (* (sin ky) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
3.8b
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
3.8b
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
3.8b
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

rewrite148.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
63×sqrt-prod
51×times-frac
43×add-sqr-sqrt
31×add-cube-cbrt
18×unpow-prod-down distribute-lft-out
10×pow1
9×rem-sqrt-square sqrt-pow1
6×associate-/r/
4×add-cbrt-cube sqrt-div add-exp-log add-log-exp
3×flip3-+ pow1/2 flip-+ div-inv pow-flip inv-pow
1×cbrt-prod cbrt-div pow1/3 associate-*r/
Counts
4 → 118
Calls
4 calls:
21.0ms
(cbrt (* (sin ky) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
50.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
40.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
32.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

series729.0ms

Counts
4 → 12
Calls
4 calls:
278.0ms
(cbrt (* (sin ky) (sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))))
140.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
162.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))
149.0ms
(sqrt (/ 1 (+ (pow (sin ky) 2) (pow (sin kx) 2))))

simplify1.9s

Counts
130 → 130
Iterations
IterNodes
done5000
33536
2782
1262
0136

prune840.0ms

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.7b

regimes2.5s

Accuracy

0% (1.7b remaining)

Error of 12.8b against oracle of 11.1b and baseline of 12.8b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done28
128
022

end0.0ms

sample9.2s

Algorithm
intervals
Results
5.1s2766×body1280valid
2.6s1903×body640valid
477.0ms2255×body80valid
452.0ms713×body320valid
307.0ms363×body160valid