Details

sample797.0ms

Algorithm

intervals

Results

524.0ms	53×	body	640	valid
139.0ms	90×	body	1280	valid
17.0ms	22×	body	320	valid
15.0ms	79×	body	80	valid
5.0ms	12×	body	160	valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4952
6	1182
5	304
4	132
3	66
2	39
1	23
0	13

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.8b

localize49.0ms

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)
3.2b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite203.0ms

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:

114.0ms	(* (/ (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)
66.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series679.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
163.0ms	(pow (sin kx) 2.0)
148.0ms	(pow (sin ky) 2.0)
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.0s

Counts

130 → 130

Iterations

Iter	Nodes
done	5000
3	4224
2	1321
1	456
0	189

prune1.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.3b

localize44.0ms

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))

rewrite26.0ms

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))

series841.0ms

Counts

3 → 9

Calls

3 calls:

169.0ms	(hypot (sin ky) (sin kx))
291.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
381.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify2.1s

Counts

82 → 82

Iterations

Iter	Nodes
done	5007
3	2899
2	970
1	304
0	132

prune663.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.3b

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(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)))

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))
27.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
13.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series845.0ms

Counts

3 → 9

Calls

3 calls:

212.0ms	(hypot (sin ky) (sin kx))
295.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
338.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify2.2s

Counts

82 → 82

Iterations

Iter	Nodes
done	5009
3	2552
2	887
1	278
0	122

prune733.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.3b

localize64.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (hypot (sin ky) (sin kx)))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))
0.6b	(cbrt (sin ky))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (hypot (sin ky) (sin kx)))
1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))
1.0ms	(cbrt (sin ky))

series632.0ms

Counts

4 → 12

Calls

4 calls:

247.0ms	(cbrt (hypot (sin ky) (sin kx)))
147.0ms	(cbrt (sin ky))
131.0ms	(cbrt (sin ky))
107.0ms	(cbrt (sin ky))

simplify2.3s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
4	3325
3	983
2	347
1	143
0	68

prune534.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.3b

regimes1.7s

Accuracy

0% (1.0b remaining)

Error of 9.5b against oracle of 8.5b and baseline of 9.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample9.6s

Algorithm

intervals

Results

5.3s	2744×	body	1280	valid
2.4s	1836×	body	640	valid
796.0ms	2241×	body	80	valid
498.0ms	805×	body	320	valid
198.0ms	374×	body	160	valid