Details

sample616.0ms

Algorithm

intervals

Results

121.0ms	77×	body	1280	valid
77.0ms	66×	body	640	valid
64.0ms	78×	body	80	valid
13.0ms	20×	body	320	valid
9.0ms	15×	body	160	valid

simplify987.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2046
7	2046
6	911
5	367
4	177
3	95
2	61
1	25
0	13

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize39.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

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))
13.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
17.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series777.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(hypot (sin ky) (sin kx))
377.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
231.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	2005
3	2005
2	1013
1	306
0	133

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite70.0ms

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))
10.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
15.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
38.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))

series927.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(hypot (sin ky) (sin kx))
206.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
213.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
332.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))

simplify1.3s

Counts

208 → 208

Iterations

Iter	Nodes
done	2000
3	2000
2	1785
1	737
0	280

prune2.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.1b	(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)))

rewrite21.0ms

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

series714.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(hypot (sin ky) (sin kx))
204.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
349.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify1.6s

Counts

123 → 123

Iterations

Iter	Nodes
done	2000
3	2000
2	1475
1	482
0	203

prune1.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.0b

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

480×	`times-frac`
239×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
60×	`associate-/r*`
36×	`add-exp-log`
23×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
10×	`cbrt-undiv`
9×	`associate-/l*`
6×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`hypot-udef` `pow-flip` `inv-pow`

Counts

4 → 323

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
14.0ms	(/ 1 (/ (sin ky) (hypot (sin ky) (sin kx))))
34.0ms	(/ (sin th) (/ 1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
16.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series980.0ms

Counts

4 → 12

Calls

4 calls:

183.0ms	(hypot (sin ky) (sin kx))
190.0ms	(/ 1 (/ (sin ky) (hypot (sin ky) (sin kx))))
350.0ms	(/ (sin th) (/ 1 (/ (sin ky) (hypot (sin ky) (sin kx)))))
257.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.1s

Counts

335 → 335

Iterations

Iter	Nodes
done	2035
2	2035
1	1381
0	510

prune4.7s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.0b

regimes990.0ms

Accuracy

0% (0.2b remaining)

Error of 8.5b against oracle of 8.3b and baseline of 8.5b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	13
1	13
0	11

end0.0ms

sample11.7s

Algorithm

intervals

Results

6.9s	2775×	body	1280	valid
2.8s	1779×	body	640	valid
765.0ms	2313×	body	80	valid
735.0ms	796×	body	320	valid
187.0ms	337×	body	160	valid