Details

sample327.0ms

Algorithm

intervals

Results

129.0ms	81×	body	1280	valid
39.0ms	56×	body	640	valid
16.0ms	34×	body	320	valid
11.0ms	76×	body	80	valid
3.0ms	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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 3 expressions with local error:

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

rewrite25.0ms

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))))
9.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series737.0ms

Counts

3 → 9

Calls

3 calls:

159.0ms	(hypot (sin ky) (sin kx))
335.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
242.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.0s

Counts

85 → 85

Iterations

Iter	Nodes
done	5003
3	2946
2	1013
1	306
0	133

prune635.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

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))
32.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
7.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

series941.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(hypot (sin ky) (sin kx))
243.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
315.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))
233.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify2.0s

Counts

208 → 208

Iterations

Iter	Nodes
done	5000
2	2173
1	737
0	280

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.9b

localize36.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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))
10.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
10.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

series862.0ms

Counts

3 → 9

Calls

3 calls:

193.0ms	(hypot (sin ky) (sin kx))
249.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
420.0ms	(/ (sin th) (/ (hypot (sin ky) (sin kx)) (sin ky)))

simplify1.5s

Counts

123 → 123

Iterations

Iter	Nodes
done	5001
2	1475
1	482
0	203

prune976.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.9b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
0.1b	(* (sin th) (log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))))
0.1b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.3b	(expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
9.0ms	(* (sin th) (log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))))
7.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.0ms	(expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))

series1.2s

Counts

4 → 12

Calls

4 calls:

260.0ms	(log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky)))))
363.0ms	(* (sin th) (log1p (expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))))
261.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
310.0ms	(expm1 (/ (sin ky) (hypot (sin kx) (sin ky))))

simplify2.0s

Counts

87 → 87

Iterations

Iter	Nodes
done	5000
3	1958
2	780
1	274
0	136

prune531.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.9b

regimes1.5s

Accuracy

0% (0.2b remaining)

Error of 8.6b against oracle of 8.4b and baseline of 8.6b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	9
0	9

end0.0ms

sample9.0s

Algorithm

intervals

Results

4.9s	2678×	body	1280	valid
2.2s	1840×	body	640	valid
658.0ms	779×	body	320	valid
633.0ms	2358×	body	80	valid
318.0ms	345×	body	160	valid