Details

Time bar (total: 23.5s)

sample312.0ms

Algorithm
intervals
Results
159.0ms89×body1280valid
48.0ms63×body640valid
13.0ms24×body320valid
12.0ms74×body80valid
2.0ms6×body160valid

simplify1.0s

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

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
34×add-sqr-sqrt
30×associate-*l*
26×times-frac
25×add-cube-cbrt
21×sqrt-prod
14×unpow-prod-down
11×add-exp-log
9×pow1 add-cbrt-cube
8×distribute-lft-out
6×pow-unpow
4×sqrt-div add-log-exp
3×associate-*r* unswap-sqr
2×pow-to-exp pow-pow flip3-+ pow-exp prod-exp associate-/r/ cbrt-unprod flip-+ sqr-pow
1×cbrt-undiv rem-sqrt-square sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
114.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
5.0ms
(pow (sin kx) 2.0)
5.0ms
(pow (sin ky) 2.0)
46.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series720.0ms

Counts
4 → 12
Calls
4 calls:
228.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
160.0ms
(pow (sin kx) 2.0)
194.0ms
(pow (sin ky) 2.0)
137.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify914.0ms

Counts
113 → 113
Iterations
IterNodes
done5000
21861
1451
0181

prune870.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite75.0ms

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:
31.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
5.0ms
(pow (sin kx) 2.0)
11.0ms
(pow (sin ky) 2.0)
25.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series636.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
171.0ms
(pow (sin kx) 2.0)
151.0ms
(pow (sin ky) 2.0)
111.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify711.0ms

Counts
112 → 112
Iterations
IterNodes
done5001
21454
1382
0175

prune754.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 10.5b

localize36.0ms

Local error

Found 4 expressions with local error:

2.6b
(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
14.4b
(cbrt (pow (sin kx) 2.0))
14.4b
(cbrt (pow (sin kx) 2.0))
14.4b
(cbrt (pow (sin kx) 2.0))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
21×cbrt-prod
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×unpow-prod-down
5×pow1
4×add-cbrt-cube add-exp-log add-log-exp
3×pow1/3 sqrt-prod sqr-pow
2×sqrt-div
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 60
Calls
4 calls:
83.0ms
(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
4.0ms
(cbrt (pow (sin kx) 2.0))
5.0ms
(cbrt (pow (sin kx) 2.0))
5.0ms
(cbrt (pow (sin kx) 2.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
105.0ms
(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
329.0ms
(cbrt (pow (sin kx) 2.0))
331.0ms
(cbrt (pow (sin kx) 2.0))
345.0ms
(cbrt (pow (sin kx) 2.0))

simplify973.0ms

Counts
72 → 72
Iterations
IterNodes
done5000
31942
2526
1207
096

prune807.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 10.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
2.6b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite127.0ms

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×flip3-+ add-cbrt-cube add-exp-log 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:
14.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
42.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
47.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
22.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series627.0ms

Counts
4 → 12
Calls
4 calls:
249.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
133.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
118.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
127.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.5s

Counts
102 → 102
Iterations
IterNodes
done5000
33607
2844
1289
0160

prune667.0ms

Pruning

21 alts after pruning (19 fresh and 2 done)

Merged error: 10.5b

regimes1.7s

Accuracy

0% (1.3b remaining)

Error of 12.5b against oracle of 11.2b and baseline of 12.5b

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done15
115
013

end0.0ms

sample9.5s

Algorithm
intervals
Results
5.8s2753×body1280valid
2.1s1802×body640valid
522.0ms769×body320valid
436.0ms2311×body80valid
173.0ms365×body160valid