Details

sample305.0ms

Algorithm

intervals

Results

125.0ms	75×	body	1280	valid
57.0ms	69×	body	640	valid
15.0ms	81×	body	80	valid
12.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify2.5s

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.5b

localize43.0ms

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))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 86

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
56.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series696.0ms

Counts

3 → 9

Calls

3 calls:

145.0ms	(hypot (sin ky) (sin kx))
226.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
325.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify2.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5002
3	3195
2	1069
1	326
0	139

prune560.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.3b

localize23.0ms

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 84

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
32.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

series713.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(hypot (sin ky) (sin kx))
229.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
307.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))

simplify2.1s

Counts

93 → 93

Iterations

Iter	Nodes
done	5000
3	2963
2	1000
1	332
0	141

prune718.0ms

Pruning

18 alts after pruning (17 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	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
0.2b	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
116×	`add-sqr-sqrt`
105×	`*-un-lft-identity`
102×	`add-cube-cbrt`
52×	`associate-l`
36×	`add-exp-log`
35×	`associate-/r*`
20×	`add-cbrt-cube`
19×	`associate-*l/`
18×	`associate-/r/`
16×	`associate-/l*`
15×	`div-exp`
11×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`clear-num`
5×	`frac-2neg` `unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`remove-double-div`
1×	`hypot-udef` `pow-prod-down` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 231

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
12.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
84.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
26.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series1.0s

Counts

4 → 12

Calls

4 calls:

159.0ms	(hypot (sin ky) (sin kx))
193.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
376.0ms	(* (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))) (sin th))
306.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify2.2s

Counts

243 → 243

Iterations

Iter	Nodes
done	5000
2	2428
1	808
0	304

prune1.5s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.3b

localize45.0ms

Local error

Found 3 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
55×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
19×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r/` `associate-/l*`
6×	`div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `clear-num` `frac-2neg` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`hypot-udef`

Counts

3 → 122

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
13.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
30.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series770.0ms

Counts

3 → 9

Calls

3 calls:

173.0ms	(hypot (sin ky) (sin kx))
215.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
382.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify2.2s

Counts

131 → 131

Iterations

Iter	Nodes
done	5001
2	1506
1	493
0	208

prune799.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 7.3b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	10
1	10
0	9

end0.0ms

sample11.2s

Algorithm

intervals

Results

6.4s	2645×	body	1280	valid
2.8s	1839×	body	640	valid
789.0ms	2387×	body	80	valid
667.0ms	775×	body	320	valid
251.0ms	354×	body	160	valid