Details

sample1.1s

Algorithm

intervals

Results

761.0ms	61×	body	640	valid
143.0ms	88×	body	1280	valid
12.0ms	76×	body	80	valid
9.0ms	19×	body	320	valid
3.0ms	12×	body	160	valid

simplify5.1s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	39	16
3	68	16
4	152	16
5	333	16
6	1049	16
7	4305	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
39×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
22×	`unpow-prod-down`
10×	`distribute-lft-out`
9×	`hypot-def`
8×	`add-exp-log` `associate-/r*` `sqr-pow`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 117

Calls

4 calls:

47.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
5.0ms	(pow (sin ky) 2.0)
49.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series690.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
184.0ms	(pow (sin kx) 2.0)
170.0ms	(pow (sin ky) 2.0)
126.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

129 → 129

Iterations

Useful iterations: 3 (756.0ms)

Iter	Nodes	Cost
0	178	1808
1	340	1625
2	850	1557
3	2640	1556
done	5000	1556

prune737.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.8b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

0.0ms	(hypot (sin ky) (sin kx))
28.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
18.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series773.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms	(hypot (sin ky) (sin kx))
332.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
286.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (942.0ms)

Iter	Nodes	Cost
0	130	1126
1	284	1106
2	790	987
3	2333	984
done	5000	984

prune447.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.7b

localize24.0ms

Local error

Found 3 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 73

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
18.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
41.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

series848.0ms

Counts

3 → 9

Calls

3 calls:

195.0ms	(hypot (sin ky) (sin kx))
337.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
316.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))

simplify2.3s

Counts

82 → 82

Iterations

Useful iterations: 3 (968.0ms)

Iter	Nodes	Cost
0	121	1123
1	252	1091
2	782	976
3	2471	975
done	5000	975

prune434.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 7.7b

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

1.0ms	(hypot (sin ky) (sin kx))
19.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
52.0ms	(* (sin ky) (* 1 (/ (sin th) (hypot (sin ky) (sin kx)))))

series767.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms	(hypot (sin ky) (sin kx))
272.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))
288.0ms	(* (sin ky) (* 1 (/ (sin th) (hypot (sin ky) (sin kx)))))

simplify2.7s

Counts

73 → 73

Iterations

Useful iterations: 3 (628.0ms)

Iter	Nodes	Cost
0	128	1053
1	252	964
2	643	826
3	1715	825
done	5000	825

prune290.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 7.7b

regimes850.0ms

Accuracy

0% (0.2b remaining)

Error of 8.5b against oracle of 8.4b and baseline of 8.5b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	11	13
1	15	11
done	15	11

end0.0ms

sample5.4s

Algorithm

intervals

Results

3.0s	2761×	body	1280	valid
1.2s	1851×	body	640	valid
341.0ms	734×	body	320	valid
311.0ms	2326×	body	80	valid
95.0ms	328×	body	160	valid