Details

sample380.0ms

Algorithm

intervals

Results

158.0ms	75×	body	1280	valid
69.0ms	69×	body	640	valid
18.0ms	81×	body	80	valid
14.0ms	22×	body	320	valid
4.0ms	9×	body	160	valid

simplify2.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	3205
6	911
5	367
4	177
3	95
2	61
1	25
0	13

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.5b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin ky) (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite26.0ms

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` `insert-posit16` `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 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
8.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
15.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series720.0ms

Counts

3 → 9

Calls

3 calls:

158.0ms	(hypot (sin ky) (sin kx))
181.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
381.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify2.3s

Counts

85 → 85

Iterations

Iter	Nodes
done	5017
3	3345
2	1003
1	305
0	133

prune718.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.3b

localize46.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.2b	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
0.2b	(* (sin th) (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt`
7×	`associate-r`
6×	`times-frac` `div-exp`
5×	`pow1` `cbrt-unprod`
4×	`cbrt-undiv`
3×	`expm1-log1p-u` `associate-l` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`1-exp` `div-inv`
1×	`hypot-udef` `clear-num` `associate-/r` `frac-2neg` `pow-prod-down` `associate-r/` `*-commutative` `unswap-sqr`

Counts

3 → 67

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
16.0ms	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
46.0ms	(* (sin th) (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))))

series693.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(hypot (sin ky) (sin kx))
215.0ms	(/ (sin ky) (* 1 (hypot (sin ky) (sin kx))))
317.0ms	(* (sin th) (/ (sin ky) (* 1 (hypot (sin ky) (sin kx)))))

simplify2.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5008
3	3066
2	1123
1	323
0	132

prune464.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sin ky) (sin kx))
0.1b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
0.2b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-r`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`hypot-udef` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `pow-flip` `inv-pow`

Counts

4 → 196

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
11.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
45.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
12.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series997.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(hypot (sin ky) (sin kx))
201.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
350.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
268.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify2.2s

Counts

208 → 208

Iterations

Iter	Nodes
done	5000
2	2173
1	737
0	280

prune1.3s

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (sin ky))
0.2b	(/ 1 (/ 1 (sin ky)))
0.3b	(/ (sin th) (hypot (sin kx) (sin ky)))
0.3b	(* (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (/ 1 (sin ky))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

195×	`times-frac`
149×	`add-sqr-sqrt`
114×	`*-un-lft-identity`
108×	`add-exp-log`
104×	`add-cube-cbrt`
58×	`div-exp`
44×	`associate-r`
34×	`add-cbrt-cube`
26×	`prod-exp`
22×	`rec-exp` `1-exp`
19×	`associate-/r*`
14×	`cbrt-undiv` `unswap-sqr`
13×	`associate-l`
12×	`div-inv`
9×	`pow1` `associate-/l*`
6×	`cbrt-unprod`
5×	`pow-flip`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `inv-pow`
2×	`associate-/r/`
1×	`frac-times` `pow-prod-down` `associate-l/` `associate-r/` `un-div-inv` `*-commutative` `remove-double-div`

Counts

4 → 271

Calls

4 calls:

6.0ms	(/ 1 (sin ky))
8.0ms	(/ 1 (/ 1 (sin ky)))
11.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
24.0ms	(* (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (/ 1 (sin ky))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ 1 (sin ky))
8.0ms	(/ 1 (/ 1 (sin ky)))
241.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
307.0ms	(* (/ (sin th) (hypot (sin kx) (sin ky))) (/ 1 (/ 1 (sin ky))))

simplify1.7s

Counts

283 → 283

Iterations

Iter	Nodes
done	5061
2	2067
1	957
0	332

prune1.1s

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 7.3b

regimes1.7s

Accuracy

0% (0.2b remaining)

Error of 8.8b against oracle of 8.7b and baseline of 8.8b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	11

end0.0ms

sample11.5s

Algorithm

intervals

Results

6.1s	2645×	body	1280	valid
3.2s	1839×	body	640	valid
778.0ms	775×	body	320	valid
730.0ms	2387×	body	80	valid
341.0ms	354×	body	160	valid