Details

sample399.0ms

Algorithm

intervals

Results

145.0ms	91×	body	1280	valid
90.0ms	28×	body	320	valid
61.0ms	58×	body	640	valid
14.0ms	64×	body	80	valid
6.0ms	15×	body	160	valid

simplify4.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize38.0ms

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)
2.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite139.0ms

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:

69.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
18.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
36.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
177.0ms	(pow (sin kx) 2.0)
147.0ms	(pow (sin ky) 2.0)
167.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

129 → 129

Iterations

Useful iterations: 3 (762.0ms)

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

prune664.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize16.0ms

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)))

rewrite54.0ms

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:

1.0ms	(hypot (sin ky) (sin kx))
39.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
11.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series817.0ms

Counts

3 → 9

Calls

3 calls:

170.0ms	(hypot (sin ky) (sin kx))
354.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
292.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify2.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (766.0ms)

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

prune421.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.2b

localize23.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

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:

0.0ms	(hypot (sin ky) (sin kx))
24.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
9.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

series782.0ms

Counts

3 → 9

Calls

3 calls:

167.0ms	(hypot (sin ky) (sin kx))
324.0ms	(* (sin ky) (/ (sin th) (hypot (sin ky) (sin kx))))
290.0ms	(/ (sin th) (hypot (sin ky) (sin kx)))

simplify2.3s

Counts

82 → 82

Iterations

Useful iterations: 3 (886.0ms)

Iter	Nodes	Cost
0	121	1123
1	252	1091
2	774	976
3	2468	975
done	5001	975

prune474.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
0.4b	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

103×	`cbrt-prod`
81×	`add-sqr-sqrt`
69×	`times-frac`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 152

Calls

4 calls:

39.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
3.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

series1.4s

Counts

4 → 12

Calls

4 calls:

382.0ms	(* (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))) (cbrt (/ (sin ky) (hypot (sin ky) (sin kx)))))
387.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
310.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))
334.0ms	(cbrt (/ (sin ky) (hypot (sin ky) (sin kx))))

simplify4.3s

Counts

164 → 164

Iterations

Useful iterations: done (4.3s)

Iter	Nodes	Cost
0	171	3641
1	290	3469
2	755	3314
3	1550	3076
4	4046	3045
done	5000	2977

prune944.0ms

Pruning

22 alts after pruning (20 fresh and 2 done)

Merged error: 7.2b

Details

sample399.0ms

simplify4.9s

prune9.0ms

localize38.0ms

rewrite139.0ms

series719.0ms

simplify1.9s

prune664.0ms

localize16.0ms

rewrite54.0ms

series817.0ms

simplify2.1s

prune421.0ms

localize23.0ms

rewrite36.0ms

series782.0ms

simplify2.3s

prune474.0ms

localize29.0ms

rewrite60.0ms

series1.4s

simplify4.3s

prune944.0ms

regimes18.0ms