Details

Time bar (total: 29.0s)

sample307.0ms

Algorithm
intervals
Results
147.0ms91×body1280valid
34.0ms57×body640valid
9.0ms69×body80valid
9.0ms21×body320valid
5.0ms18×body160valid

simplify2.4s

Counts
1 → 1
Iterations
IterNodes
done5000
73205
6911
5367
4177
395
261
125
013

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.6b

localize33.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot (sin ky) (sin kx))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite27.0ms

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))
8.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
16.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series775.0ms

Counts
3 → 9
Calls
3 calls:
146.0ms
(hypot (sin ky) (sin kx))
236.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
393.0ms
(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify2.1s

Counts
85 → 85
Iterations
IterNodes
done5017
33345
21003
1305
0133

prune662.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.5b

localize57.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b
(* (sin th) (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))))
0.3b
(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv expm1-udef unswap-sqr
Counts
4 → 75
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
16.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
18.0ms
(* (sin th) (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))))
1.0ms
(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.2s

Counts
4 → 12
Calls
4 calls:
280.0ms
(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
276.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
354.0ms
(* (sin th) (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))))
266.0ms
(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.9s

Counts
87 → 87
Iterations
IterNodes
done5000
31949
2778
1275
0136

prune757.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b
(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.2b
(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b
(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
0.3b
(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac
8×add-cbrt-cube add-exp-log
6×pow1
5×log1p-expm1-u
4×expm1-log1p-u insert-posit16 add-log-exp
3×associate-/r* associate-*r* associate-*l* associate-/l*
1×cbrt-undiv log1p-udef expm1-log1p clear-num frac-2neg div-exp pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod div-inv expm1-udef unswap-sqr
Counts
4 → 75
Calls
4 calls:
0.0ms
(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
16.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
17.0ms
(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
1.0ms
(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.2s

Counts
4 → 12
Calls
4 calls:
324.0ms
(log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
227.0ms
(/ (sin ky) (hypot (sin ky) (sin kx)))
316.0ms
(* (log1p (expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))) (sin th))
324.0ms
(expm1 (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.9s

Counts
87 → 87
Iterations
IterNodes
done5000
31901
2734
1271
0137

prune659.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.5b

localize39.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt
84×times-frac
61×*-un-lft-identity add-cube-cbrt
51×sqrt-prod
22×associate-*r* associate-*l*
20×add-cbrt-cube add-exp-log
12×associate-/r*
9×unswap-sqr
7×pow1
6×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
2×clear-num frac-2neg
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ *-commutative
Counts
4 → 176
Calls
4 calls:
1.0ms
(sqrt (hypot (sin ky) (sin kx)))
14.0ms
(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
45.0ms
(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
9.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

series1.4s

Counts
4 → 12
Calls
4 calls:
176.0ms
(sqrt (hypot (sin ky) (sin kx)))
270.0ms
(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
296.0ms
(* (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (/ (sin ky) (sqrt (hypot (sin ky) (sin kx)))))
641.0ms
(/ (sin ky) (sqrt (hypot (sin ky) (sin kx))))

simplify2.1s

Counts
188 → 188
Iterations
IterNodes
done5000
21923
1591
0225

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.5b

regimes1.3s

Accuracy

0% (0.2b remaining)

Error of 9.2b against oracle of 9.0b and baseline of 9.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done15
115
011

end0.0ms

sample9.1s

Algorithm
intervals
Results
4.6s2735×body1280valid
2.4s1852×body640valid
989.0ms2264×body80valid
650.0ms766×body320valid
142.0ms383×body160valid