Details

sample372.0ms

Algorithm

intervals

Results

128.0ms	85×	body	1280	valid
106.0ms	62×	body	640	valid
15.0ms	75×	body	80	valid
12.0ms	19×	body	320	valid
5.0ms	15×	body	160	valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5025
7	3442
6	908
5	294
4	128
3	62
2	35
1	23
0	13

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.2b

localize38.0ms

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)
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite164.0ms

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:

122.0ms	(* (/ (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)
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series746.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
169.0ms	(pow (sin kx) 2.0)
201.0ms	(pow (sin ky) 2.0)
148.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.5s

Counts

113 → 113

Iterations

Iter	Nodes
done	5006
3	4095
2	1252
1	442
0	181

prune869.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.1b

localize43.0ms

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 ky) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite188.0ms

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:

73.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
5.0ms	(pow (sin ky) 2.0)
60.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
42.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series661.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
174.0ms	(pow (sin ky) 2.0)
188.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
97.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.9s

Counts

145 → 145

Iterations

Iter	Nodes
done	5007
3	4424
2	1250
1	463
0	195

prune985.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.1b

localize81.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(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)))))
29.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
37.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
93.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
461.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
115.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5008
3	2275
2	698
1	286
0	160

prune1.1s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 9.1b

localize164.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin ky))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
15×	`sqrt-prod`
11×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`unpow-prod-down` `sqrt-div` `distribute-lft-out`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`cbrt-prod` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
1×	`pow1/3`

Counts

4 → 62

Calls

4 calls:

1.0ms	(cbrt (sin ky))
21.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
22.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
33.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series520.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(cbrt (sin ky))
117.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
146.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
116.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.2s

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
4	4268
3	1136
2	428
1	176
0	81

prune715.0ms

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 9.1b

regimes2.6s

Accuracy

53.5% (0.8b remaining)

Error of 12.0b against oracle of 11.1b and baseline of 12.9b

bsearch6.0ms

simplify17.0ms

Iterations

Iter	Nodes
done	43
1	43
0	33

end0.0ms

sample8.7s

Algorithm

intervals

Results

4.9s	2710×	body	1280	valid
2.1s	1845×	body	640	valid
481.0ms	2312×	body	80	valid
406.0ms	766×	body	320	valid
266.0ms	367×	body	160	valid