Details

Time bar (total: 33.7s)

sample423.0ms

Algorithm
intervals
Results
216.0ms81×body1280valid
74.0ms61×body640valid
22.0ms82×body80valid
17.0ms20×body320valid
7.0ms12×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
73553
61010
5403
4186
396
261
125
013

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.4b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
19×*-un-lft-identity times-frac add-cube-cbrt
13×associate-*r*
10×add-cbrt-cube add-exp-log
5×pow1
3×expm1-log1p-u associate-/r* associate-*l* insert-posit16 log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
1×hypot-udef clear-num frac-2neg pow-prod-down associate-*r/ *-commutative
Counts
3 → 76
Calls
3 calls:
0.0ms
(hypot (sin ky) (sin kx))
20.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
11.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))

series1.3s

Counts
3 → 9
Calls
3 calls:
145.0ms
(hypot (sin ky) (sin kx))
850.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
278.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify855.0ms

Counts
85 → 85
Iterations
IterNodes
32750
2996
1304
0133

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(hypot (sin ky) (sin kx))
0.1b
(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
0.2b
(/ 1 (hypot (sin ky) (sin kx)))
0.3b
(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
28×add-sqr-sqrt
22×*-un-lft-identity
21×add-cube-cbrt
20×times-frac add-cbrt-cube
14×associate-*r*
13×prod-exp
12×pow1
7×cbrt-unprod
6×div-exp associate-*l*
4×expm1-log1p-u pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv rec-exp associate-/r* 1-exp associate-/l* unswap-sqr
2×un-div-inv *-commutative div-inv
1×hypot-udef clear-num frac-2neg pow-flip inv-pow
Counts
4 → 111
Calls
4 calls:
0.0ms
(hypot (sin ky) (sin kx))
44.0ms
(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
4.0ms
(/ 1 (hypot (sin ky) (sin kx)))
13.0ms
(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

series958.0ms

Counts
4 → 12
Calls
4 calls:
162.0ms
(hypot (sin ky) (sin kx))
372.0ms
(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
193.0ms
(/ 1 (hypot (sin ky) (sin kx)))
230.0ms
(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

simplify1.5s

Counts
123 → 123
Iterations
IterNodes
33368
21254
1391
0168

prune1.7s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.3b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1 (sqrt (hypot (sin ky) (sin kx))))
0.3b
(* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx)))))
0.3b
(* (* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx))))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.4b
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite106.0ms

Algorithm
rewrite-expression-head
Rules
76×times-frac
73×add-sqr-sqrt
63×*-un-lft-identity
61×add-cube-cbrt
54×add-exp-log
44×associate-*r* sqrt-prod
34×add-cbrt-cube
22×prod-exp
14×div-exp
13×pow1
12×associate-/r* cbrt-unprod
8×cbrt-undiv
6×associate-/l*
5×unswap-sqr
4×expm1-log1p-u rec-exp 1-exp associate-*l* pow-prod-down associate-*r/ insert-posit16 log1p-expm1-u div-inv add-log-exp
3×un-div-inv pow-flip
2×frac-times clear-num frac-2neg associate-*l/ *-commutative
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 197
Calls
4 calls:
10.0ms
(/ 1 (sqrt (hypot (sin ky) (sin kx))))
17.0ms
(* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx)))))
64.0ms
(* (* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx))))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
9.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.1s

Counts
4 → 12
Calls
4 calls:
209.0ms
(/ 1 (sqrt (hypot (sin ky) (sin kx))))
243.0ms
(* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx)))))
344.0ms
(* (* (sin th) (/ 1 (sqrt (hypot (sin ky) (sin kx))))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
255.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify814.0ms

Counts
209 → 209
Iterations
IterNodes
22065
1650
0255

prune2.9s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 9.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (hypot (sin ky) (sin kx)))
0.3b
(* (sin th) (pow (hypot (sin ky) (sin kx)) -1/2))
0.3b
(* (* (sin th) (pow (hypot (sin ky) (sin kx)) -1/2)) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
0.4b
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
36×*-un-lft-identity times-frac add-cube-cbrt
35×add-exp-log
29×associate-*r*
24×sqrt-prod
20×add-cbrt-cube
17×prod-exp
7×pow1 cbrt-unprod
6×associate-/r*
5×div-exp
4×expm1-log1p-u unpow-prod-down associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp cbrt-undiv pow-exp associate-/l* unswap-sqr
2×*-commutative div-inv sqr-pow
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/
Counts
4 → 134
Calls
4 calls:
2.0ms
(sqrt (hypot (sin ky) (sin kx)))
24.0ms
(* (sin th) (pow (hypot (sin ky) (sin kx)) -1/2))
30.0ms
(* (* (sin th) (pow (hypot (sin ky) (sin kx)) -1/2)) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
9.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.2s

Counts
4 → 12
Calls
4 calls:
217.0ms
(sqrt (hypot (sin ky) (sin kx)))
285.0ms
(* (sin th) (pow (hypot (sin ky) (sin kx)) -1/2))
396.0ms
(* (* (sin th) (pow (hypot (sin ky) (sin kx)) -1/2)) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
293.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify2.5s

Counts
146 → 146
Iterations
IterNodes
36178
21617
1526
0208

prune2.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 9.3b

regimes1.1s

Accuracy

0% (0.3b remaining)

Error of 8.6b against oracle of 8.3b and baseline of 8.6b

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
215
115
011

end0.0ms

sample12.1s

Algorithm
intervals
Results
6.8s2689×body1280valid
2.9s1867×body640valid
1.0s773×body320valid
751.0ms2328×body80valid
281.0ms343×body160valid