Details

sample384.0ms

Algorithm

intervals

Results

174.0ms	77×	body	1280	valid
77.0ms	66×	body	640	valid
17.0ms	78×	body	80	valid
16.0ms	20×	body	320	valid
7.0ms	15×	body	160	valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
7	3537
6	1018
5	404
4	185
3	94
2	59
1	25
0	13

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.3b

localize41.0ms

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)))

rewrite57.0ms

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))
35.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
17.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series781.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(hypot (sin ky) (sin kx))
346.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))
268.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify1.8s

Counts

85 → 85

Iterations

Iter	Nodes
3	2640
2	996
1	302
0	133

prune1.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.0b

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

rewrite80.0ms

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)))
48.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(hypot (sin ky) (sin kx))
205.0ms	(/ (hypot (sin ky) (sin kx)) (sin ky))
234.0ms	(/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky)))
369.0ms	(* (sin th) (/ 1 (/ (hypot (sin ky) (sin kx)) (sin ky))))

simplify10.3s

Counts

208 → 208

Iterations

Iter	Nodes
3	4948
2	1732
1	732
0	280

prune2.8s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 8.0b

localize26.0ms

Local error

Found 3 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
13×	`associate-l`
10×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
3×	`expm1-log1p-u` `associate-/r` `associate-r` `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-l/` `-commutative`

Counts

3 → 76

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
14.0ms	(* (/ (sin th) (hypot (sin ky) (sin kx))) (sin ky))
11.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series1.2s

Counts

3 → 9

Calls

3 calls:

184.0ms	(hypot (sin ky) (sin kx))
696.0ms	(* (/ (sin th) (hypot (sin ky) (sin kx))) (sin ky))
315.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify2.3s

Counts

85 → 85

Iterations

Iter	Nodes
3	2192
2	816
1	278
0	125

prune1.1s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.0b

localize47.0ms

Local error

Found 4 expressions with local error:

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

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
306×	`add-sqr-sqrt`
281×	`*-un-lft-identity` `add-cube-cbrt`
272×	`sqrt-prod`
136×	`associate-l`
25×	`associate-/l*`
20×	`add-cbrt-cube` `add-exp-log`
16×	`div-inv`
12×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `prod-exp` `cbrt-unprod`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `associate-/l/`

Counts

4 → 401

Calls

4 calls:

1.0ms	(sqrt (hypot (sin ky) (sin kx)))
24.0ms	(* (/ (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))) (sin ky))
20.0ms	(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
24.0ms	(/ (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))

series1.0s

Counts

4 → 12

Calls

4 calls:

200.0ms	(sqrt (hypot (sin ky) (sin kx)))
328.0ms	(* (/ (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx)))) (sin ky))
227.0ms	(/ (sin th) (sqrt (hypot (sin ky) (sin kx))))
283.0ms	(/ (/ (sin th) (sqrt (hypot (sin ky) (sin kx)))) (sqrt (hypot (sin ky) (sin kx))))

simplify997.0ms

Counts

413 → 413

Iterations

Iter	Nodes
2	2599
1	922
0	381

prune6.0s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 8.0b

regimes1.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample11.4s

Algorithm

intervals

Results

6.4s	2775×	body	1280	valid
2.9s	1779×	body	640	valid
934.0ms	796×	body	320	valid
711.0ms	2313×	body	80	valid
210.0ms	337×	body	160	valid