Details

sample579.0ms

Algorithm

intervals

Results

199.0ms	74×	body	80	valid
166.0ms	89×	body	1280	valid
97.0ms	63×	body	640	valid
12.0ms	24×	body	320	valid
2.0ms	6×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
5	654
4	156
3	68
2	39
1	23
0	13

prune33.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize58.0ms

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
2.6b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
20×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`distribute-lft-out` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 118

Calls

4 calls:

136.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms	(pow (sin kx) 2.0)
6.0ms	(pow (sin ky) 2.0)
34.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

256.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
183.0ms	(pow (sin kx) 2.0)
166.0ms	(pow (sin ky) 2.0)
158.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify971.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1918
1	465
0	189

prune889.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.1b	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-l`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `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-l/` `-commutative`

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
7.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
15.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series765.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(hypot (sin ky) (sin kx))
237.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
369.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify762.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1355
1	304
0	132

prune620.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.3b	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
0.3b	(/ (sin th) (hypot (sin ky) (sin kx)))

rewrite45.0ms

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` `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 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
28.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
14.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series886.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(hypot (sin ky) (sin kx))
354.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
370.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify1.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5001
2	1368
1	278
0	122

prune696.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.2b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.3b	(/ (sin ky) (/ (hypot (sin ky) (sin kx)) (sin th)))
0.3b	(/ (hypot (sin ky) (sin kx)) (sin th))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `associate-/r/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
18.0ms	(/ (sin ky) (/ (hypot (sin ky) (sin kx)) (sin th)))
5.0ms	(/ (hypot (sin ky) (sin kx)) (sin th))

series848.0ms

Counts

3 → 9

Calls

3 calls:

192.0ms	(hypot (sin ky) (sin kx))
370.0ms	(/ (sin ky) (/ (hypot (sin ky) (sin kx)) (sin th)))
286.0ms	(/ (hypot (sin ky) (sin kx)) (sin th))

simplify941.0ms

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2420
1	485
0	199

prune832.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.2b

regimes991.0ms

Accuracy

0% (0.3b remaining)

Error of 8.9b against oracle of 8.6b and baseline of 8.9b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	14
1	14
0	12

end0.0ms

sample9.4s

Algorithm

intervals

Results

5.5s	2753×	body	1280	valid
1.7s	1802×	body	640	valid
992.0ms	2311×	body	80	valid
620.0ms	769×	body	320	valid
121.0ms	365×	body	160	valid