Details

sample390.0ms

Algorithm

intervals

Results

163.0ms	81×	body	1280	valid
58.0ms	70×	body	640	valid
15.0ms	24×	body	320	valid
13.0ms	71×	body	80	valid
4.0ms	10×	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

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.4b

localize61.0ms

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))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite132.0ms

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:

69.0ms	(* (/ (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)
51.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series622.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
150.0ms	(pow (sin kx) 2.0)
147.0ms	(pow (sin ky) 2.0)
100.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify934.0ms

Counts

130 → 130

Iterations

Iter	Nodes
done	5001
2	1918
1	465
0	189

prune1.1s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

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

series846.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(hypot (sin ky) (sin kx))
269.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
399.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify832.0ms

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1355
1	304
0	132

prune788.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.0b

localize40.0ms

Local error

Found 3 expressions with local error:

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

rewrite43.0ms

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))
13.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
26.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series853.0ms

Counts

3 → 9

Calls

3 calls:

181.0ms	(hypot (sin ky) (sin kx))
311.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
361.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify1.0s

Counts

82 → 82

Iterations

Iter	Nodes
done	5000
2	1376
1	277
0	122

prune666.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.0b

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`*-un-lft-identity` `add-cube-cbrt`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-l/` `prod-exp` `associate-r/` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

52.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
4.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.3s

Counts

4 → 12

Calls

4 calls:

368.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
297.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
351.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
313.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.2s

Counts

164 → 164

Iterations

Iter	Nodes
done	5000
2	1377
1	326
0	171

prune1.4s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 9.0b

regimes1.9s

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.6b and baseline of 8.8b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample9.6s

Algorithm

intervals

Results

4.7s	2722×	body	1280	valid
2.3s	1795×	body	640	valid
1.0s	2354×	body	80	valid
889.0ms	762×	body	320	valid
182.0ms	367×	body	160	valid