Details

sample319.0ms

Algorithm

intervals

Results

157.0ms	88×	body	1280	valid
40.0ms	54×	body	640	valid
14.0ms	23×	body	320	valid
12.0ms	80×	body	80	valid
3.0ms	11×	body	160	valid

simplify8.0s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize62.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite233.0ms

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` `insert-posit16` `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 → 105

Calls

4 calls:

157.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
5.0ms	(pow (sin ky) 2.0)
10.0ms	(pow (sin kx) 2.0)
51.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

486.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
222.0ms	(pow (sin ky) 2.0)
265.0ms	(pow (sin kx) 2.0)
237.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify6.0s

Counts

117 → 117

Iterations

Iter	Nodes
done	5121
3	4013
2	1261
1	447
0	185

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.5b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (sin kx) 2.0)
0.3b	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite298.0ms

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/` `insert-posit16` `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 → 137

Calls

4 calls:

11.0ms	(pow (sin kx) 2.0)
74.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
151.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
40.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.4s

Counts

4 → 12

Calls

4 calls:

210.0ms	(pow (sin kx) 2.0)
419.0ms	(/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
526.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
237.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify7.4s

Counts

149 → 149

Iterations

Iter	Nodes
done	5003
3	4672
2	1386
1	467
0	201

prune2.0s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 10.5b

localize183.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite204.0ms

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-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 94

Calls

4 calls:

31.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
46.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
68.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
51.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series1.2s

Counts

4 → 12

Calls

4 calls:

519.0ms	(cbrt (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
234.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
177.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
223.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.7s

Counts

106 → 106

Iterations

Iter	Nodes
done	5005
3	2205
2	697
1	288
0	162

prune1.9s

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 10.5b

localize262.0ms

Local error

Found 4 expressions with local error:

3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
3.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite258.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
20×	`sqrt-prod`
12×	`add-sqr-sqrt`
8×	`pow1` `unpow-prod-down` `sqrt-div` `add-cube-cbrt` `distribute-lft-out`
4×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `add-cbrt-cube` `pow1/2` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 72

Calls

4 calls:

56.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
53.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
83.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
62.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
226.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
225.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
187.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify5.3s

Counts

84 → 84

Iterations

Iter	Nodes
done	5004
4	2488
3	715
2	297
1	119
0	55

prune1.3s

Pruning

22 alts after pruning (19 fresh and 3 done)

Merged error: 10.5b

regimes5.6s

Accuracy

0% (1.5b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	15
1	15
0	13

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.2s	2716×	body	1280	valid
2.1s	1885×	body	640	valid
500.0ms	751×	body	320	valid
418.0ms	2301×	body	80	valid
176.0ms	347×	body	160	valid