Details

Time bar (total: 31.9s)

sample496.0ms

Algorithm
intervals
Results
217.0ms48×body640valid
126.0ms84×body1280valid
22.0ms35×body320valid
15.0ms75×body80valid
9.0ms14×body160valid

simplify4.4s

Counts
1 → 1
Iterations
IterNodes
done5025
73442
6908
5294
4128
362
235
123
013

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b
(pow (sin kx) 2.0)
0.2b
(pow (sin ky) 2.0)
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite162.0ms

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:
116.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms
(pow (sin kx) 2.0)
6.0ms
(pow (sin ky) 2.0)
30.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series693.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
175.0ms
(pow (sin kx) 2.0)
128.0ms
(pow (sin ky) 2.0)
153.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.6s

Counts
113 → 113
Iterations
IterNodes
done5006
34095
21252
1442
0181

prune972.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (sin ky) 2.0)
0.3b
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.3b
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite202.0ms

Algorithm
rewrite-expression-head
Rules
72×*-un-lft-identity
50×times-frac
49×add-sqr-sqrt
41×sqrt-prod
40×add-cube-cbrt
30×associate-*r*
19×unpow-prod-down
16×distribute-lft-out
12×add-exp-log
11×add-cbrt-cube
8×pow1 associate-/r*
6×sqrt-div
4×associate-/r/ add-log-exp
3×pow-unpow flip3-+ associate-*l* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×pow-to-exp rem-sqrt-square clear-num pow-pow frac-2neg sqrt-pow1 pow1/2 pow-prod-down pow-exp associate-*r/ *-commutative sqr-pow
Counts
4 → 133
Calls
4 calls:
3.0ms
(pow (sin ky) 2.0)
111.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
53.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
30.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series734.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(pow (sin ky) 2.0)
251.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
209.0ms
(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
108.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.5s

Counts
145 → 145
Iterations
IterNodes
done5011
34314
21271
1462
0195

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.3b

localize76.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
0.7b
(cbrt (sin kx))
3.0b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite54.0ms

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:
1.0ms
(cbrt (sin kx))
2.0ms
(cbrt (sin kx))
2.0ms
(cbrt (sin kx))
47.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series523.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (sin kx))
157.0ms
(cbrt (sin kx))
136.0ms
(cbrt (sin kx))
99.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

simplify2.2s

Counts
60 → 60
Iterations
IterNodes
done5001
31677
2503
1191
081

prune613.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 9.3b

localize140.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.0b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
20×sqrt-prod
12×add-sqr-sqrt
9×add-cube-cbrt
8×cbrt-prod unpow-prod-down sqrt-div distribute-lft-out
7×pow1
4×flip3-+ add-cbrt-cube add-exp-log flip-+ add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×cbrt-div
1×pow1/3
Counts
4 → 69
Calls
4 calls:
13.0ms
(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
31.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
29.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
25.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series468.0ms

Counts
4 → 12
Calls
4 calls:
131.0ms
(cbrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
138.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
92.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
106.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts
81 → 81
Iterations
IterNodes
done5001
31353
2465
1183
087

prune709.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.3b

regimes2.2s

Accuracy

0% (1.4b remaining)

Error of 13.2b against oracle of 11.8b and baseline of 13.2b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done15
115
013

end0.0ms

sample8.8s

Algorithm
intervals
Results
4.4s2684×body1280valid
2.3s1806×body640valid
1.0s2364×body80valid
549.0ms788×body320valid
181.0ms358×body160valid