Details

sample544.0ms

Algorithm

intervals

Results

207.0ms	92×	body	1280	valid
164.0ms	53×	body	640	valid
32.0ms	29×	body	320	valid
23.0ms	72×	body	80	valid
7.0ms	10×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
7	3553
6	1010
5	403
4	186
3	96
2	61
1	25
0	13

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.3b

localize41.0ms

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 th) (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite31.0ms

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))
12.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
14.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.3s

Counts

3 → 9

Calls

3 calls:

195.0ms	(hypot (sin ky) (sin kx))
276.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
877.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.0s

Counts

85 → 85

Iterations

Iter	Nodes
3	2749
2	977
1	303
0	133

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.1b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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))
9.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
34.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
14.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series911.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(hypot (sin ky) (sin kx))
185.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
325.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
246.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify570.0ms

Counts

208 → 208

Iterations

Iter	Nodes
2	2084
1	733
0	280

prune2.7s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.1b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`hypot-udef` `associate-/r/`

Counts

3 → 114

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
5.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
11.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series724.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(hypot (sin ky) (sin kx))
177.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
388.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify1.6s

Counts

123 → 123

Iterations

Iter	Nodes
3	4405
2	1506
1	479
0	203

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 9.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(/ (hypot (sin ky) (sin kx)) (sin ky))
0.2b	(/ (/ (hypot (sin ky) (sin kx)) (sin ky)) (sin th))
0.4b	(/ 1 (/ (/ (hypot (sin ky) (sin kx)) (sin ky)) (sin th)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

477×	`times-frac`
238×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
49×	`associate-/r*`
32×	`add-exp-log`
23×	`div-inv`
20×	`add-cbrt-cube`
19×	`div-exp` `associate-/l*`
10×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `clear-num` `frac-2neg` `1-exp`
1×	`hypot-udef` `associate-/r/` `pow-flip` `inv-pow` `associate-/l/`

Counts

4 → 317

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
7.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
20.0ms	(/ (/ (hypot (sin ky) (sin kx)) (sin ky)) (sin th))
22.0ms	(/ 1 (/ (/ (hypot (sin ky) (sin kx)) (sin ky)) (sin th)))

series983.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(hypot (sin ky) (sin kx))
205.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
290.0ms	(/ (/ (hypot (sin ky) (sin kx)) (sin ky)) (sin th))
301.0ms	(/ 1 (/ (/ (hypot (sin ky) (sin kx)) (sin ky)) (sin th)))

simplify1.9s

Counts

329 → 329

Iterations

Iter	Nodes
2	3371
1	1275
0	484

prune4.1s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 9.1b

regimes1.5s

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
1	9
0	9

end0.0ms

sample12.5s

Algorithm

intervals

Results

7.4s	2805×	body	1280	valid
3.2s	1823×	body	640	valid
807.0ms	784×	body	320	valid
603.0ms	2234×	body	80	valid
194.0ms	354×	body	160	valid