Details

sample417.0ms

Algorithm

intervals

Results

210.0ms	95×	body	1280	valid
69.0ms	56×	body	640	valid
20.0ms	23×	body	320	valid
18.0ms	70×	body	80	valid
7.0ms	12×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

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

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.2b

localize42.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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))
15.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
29.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

series737.0ms

Counts

3 → 9

Calls

3 calls:

161.0ms	(hypot (sin ky) (sin kx))
230.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))
345.0ms	(* (sin th) (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify1.6s

Counts

85 → 85

Iterations

Iter	Nodes
3	2773
2	977
1	301
0	133

prune1.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
0.1b	(log1p (hypot (sin ky) (sin kx)))
0.2b	(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))))
0.3b	(expm1 (log1p (hypot (sin ky) (sin kx))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

10.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
1.0ms	(log1p (hypot (sin ky) (sin kx)))
21.0ms	(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))))
0.0ms	(expm1 (log1p (hypot (sin ky) (sin kx))))

series976.0ms

Counts

4 → 12

Calls

4 calls:

285.0ms	(/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx)))))
190.0ms	(log1p (hypot (sin ky) (sin kx)))
290.0ms	(* (sin th) (/ (sin ky) (expm1 (log1p (hypot (sin ky) (sin kx))))))
211.0ms	(expm1 (log1p (hypot (sin ky) (sin kx))))

simplify1.8s

Counts

101 → 101

Iterations

Iter	Nodes
3	2710
2	1039
1	336
0	151

prune1.5s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (sin ky) (sin kx))
0.2b	(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
0.2b	(/ 1 (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
28×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
21×	`add-cube-cbrt`
20×	`times-frac` `add-cbrt-cube`
14×	`associate-r`
13×	`prod-exp`
12×	`pow1`
7×	`cbrt-unprod`
6×	`div-exp` `associate-l`
4×	`expm1-log1p-u` `pow-prod-down` `associate-*r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `associate-/r` `1-exp` `associate-/l` `unswap-sqr`
2×	`un-div-inv` `*-commutative` `div-inv`
1×	`hypot-udef` `clear-num` `frac-2neg` `pow-flip` `inv-pow`

Counts

4 → 111

Calls

4 calls:

0.0ms	(hypot (sin ky) (sin kx))
43.0ms	(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
4.0ms	(/ 1 (hypot (sin ky) (sin kx)))
14.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

series986.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(hypot (sin ky) (sin kx))
371.0ms	(* (sin th) (* (sin ky) (/ 1 (hypot (sin ky) (sin kx)))))
195.0ms	(/ 1 (hypot (sin ky) (sin kx)))
243.0ms	(* (sin ky) (/ 1 (hypot (sin ky) (sin kx))))

simplify2.8s

Counts

123 → 123

Iterations

Iter	Nodes
3	3277
2	1224
1	390
0	168

prune1.6s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 8.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (hypot (sin ky) (sin kx)))
0.2b	(/ 1 (hypot (sin ky) (sin kx)))
0.3b	(* (sin ky) (* (sqrt (/ 1 (hypot (sin ky) (sin kx)))) (sqrt (/ 1 (hypot (sin ky) (sin kx))))))
0.5b	(* (sqrt (/ 1 (hypot (sin ky) (sin kx)))) (sqrt (/ 1 (hypot (sin ky) (sin kx)))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

98×	`add-sqr-sqrt`
82×	`sqrt-prod`
70×	`times-frac`
63×	`*-un-lft-identity`
53×	`add-cube-cbrt`
34×	`pow1`
24×	`sqrt-pow1`
20×	`swap-sqr`
19×	`associate-l` `add-exp-log`
17×	`associate-r` `unswap-sqr`
15×	`add-cbrt-cube`
10×	`pow-flip` `inv-pow`
9×	`pow-prod-up`
8×	`pow1/2` `sqrt-div` `pow-prod-down` `div-inv`
6×	`associate-/r` `associate-/l`
5×	`associate-*r/` `pow-sqr`
4×	`expm1-log1p-u` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`frac-times` `cbrt-undiv` `rec-exp` `clear-num` `frac-2neg` `1-exp` `associate-l/` `-commutative`
1×	`pow2` `rem-square-sqrt` `pow-plus` `sqrt-unprod`

Counts

4 → 200

Calls

4 calls:

4.0ms	(/ 1 (hypot (sin ky) (sin kx)))
4.0ms	(/ 1 (hypot (sin ky) (sin kx)))
39.0ms	(* (sin ky) (* (sqrt (/ 1 (hypot (sin ky) (sin kx)))) (sqrt (/ 1 (hypot (sin ky) (sin kx))))))
15.0ms	(* (sqrt (/ 1 (hypot (sin ky) (sin kx)))) (sqrt (/ 1 (hypot (sin ky) (sin kx)))))

series911.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ 1 (hypot (sin ky) (sin kx)))
204.0ms	(/ 1 (hypot (sin ky) (sin kx)))
270.0ms	(* (sin ky) (* (sqrt (/ 1 (hypot (sin ky) (sin kx)))) (sqrt (/ 1 (hypot (sin ky) (sin kx))))))
197.0ms	(* (sqrt (/ 1 (hypot (sin ky) (sin kx)))) (sqrt (/ 1 (hypot (sin ky) (sin kx)))))

simplify1.2s

Counts

212 → 212

Iterations

Iter	Nodes
3	2326
2	885
1	413
0	217

prune3.3s

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 8.0b

regimes1.0s

Accuracy

0% (0.3b remaining)

Error of 8.8b against oracle of 8.6b and baseline of 8.8b

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
2	12
1	12
0	11

end0.0ms

sample11.9s

Algorithm

intervals

Results

6.2s	2705×	body	1280	valid
3.5s	1861×	body	640	valid
846.0ms	752×	body	320	valid
823.0ms	2349×	body	80	valid
186.0ms	333×	body	160	valid