Details

Time bar (total: 31.9s)

sample526.0ms

Algorithm
intervals
Results
337.0ms84×body1280valid
44.0ms61×body640valid
12.0ms27×body320valid
11.0ms70×body80valid
5.0ms14×body160valid

simplify3.7s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.8b

localize40.0ms

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))
0.3b
(pow (sin kx) 2.0)
0.3b
(pow (sin ky) 2.0)
1.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite136.0ms

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:
67.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms
(pow (sin kx) 2.0)
3.0ms
(pow (sin ky) 2.0)
59.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series667.0ms

Counts
4 → 12
Calls
4 calls:
247.0ms
(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
169.0ms
(pow (sin kx) 2.0)
134.0ms
(pow (sin ky) 2.0)
117.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.8s

Counts
113 → 113
Iterations
IterNodes
done5006
34095
21252
1442
0181

prune851.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.2b

localize57.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin ky) (/ (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)
1.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
34×add-sqr-sqrt
30×associate-*r*
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-*l* 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-*r/ *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
90.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
12.0ms
(pow (sin kx) 2.0)
6.0ms
(pow (sin ky) 2.0)
43.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
161.0ms
(pow (sin kx) 2.0)
130.0ms
(pow (sin ky) 2.0)
105.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.8s

Counts
113 → 113
Iterations
IterNodes
done5043
34411
21415
1499
0196

prune766.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 12.2b

localize95.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
0.6b
(cbrt (sin kx))
1.8b
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

rewrite55.0ms

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:
3.0ms
(cbrt (sin kx))
2.0ms
(cbrt (sin kx))
2.0ms
(cbrt (sin kx))
46.0ms
(sqrt (+ (* (pow (* (cbrt (sin kx)) (cbrt (sin kx))) 2.0) (pow (cbrt (sin kx)) 2.0)) (pow (sin ky) 2.0)))

series543.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(cbrt (sin kx))
134.0ms
(cbrt (sin kx))
160.0ms
(cbrt (sin kx))
117.0ms
(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

prune714.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 12.2b

localize107.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.8b
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite136.0ms

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:
28.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
34.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
26.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
44.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
105.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
146.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
122.0ms
(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts
102 → 102
Iterations
IterNodes
done5008
32275
2698
1286
0160

prune845.0ms

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 12.2b

regimes2.7s

Accuracy

0% (1.5b remaining)

Error of 12.7b against oracle of 11.2b and baseline of 12.7b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample8.7s

Algorithm
intervals
Results
4.4s2685×body1280valid
2.4s1872×body640valid
871.0ms755×body320valid
614.0ms2332×body80valid
124.0ms356×body160valid