Details

sample1.0s

Algorithm

intervals

Results

530.0ms	57×	body	640	valid
208.0ms	93×	body	1280	valid
19.0ms	81×	body	80	valid
12.0ms	20×	body	320	valid
2.0ms	5×	body	160	valid

simplify5.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	764
1	23	764
2	35	764
3	62	764
4	128	764
5	294	764
6	908	764
7	3442	764
done	5025	764

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

102.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
6.0ms	(pow (sin ky) 2.0)
6.0ms	(pow (sin kx) 2.0)
46.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series676.0ms

Counts

4 → 12

Calls

4 calls:

236.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
164.0ms	(pow (sin ky) 2.0)
155.0ms	(pow (sin kx) 2.0)
120.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify4.8s

Counts

113 → 113

Iterations

Useful iterations: 3 (2.8s)

Iter	Nodes	Cost
0	181	74679
1	442	69848
2	1238	69476
3	4142	69436
done	5006	69436

prune1.0s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 13.0b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
0.2b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
4.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
34×	`add-sqr-sqrt`
30×	`associate-r`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
14×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube`
8×	`distribute-lft-out`
6×	`pow-unpow`
4×	`sqrt-div` `add-log-exp`
3×	`associate-l` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `div-inv`

Counts

4 → 101

Calls

4 calls:

101.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
6.0ms	(pow (sin ky) 2.0)
5.0ms	(pow (sin kx) 2.0)
32.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series693.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(* (sin ky) (/ (sin th) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
190.0ms	(pow (sin ky) 2.0)
139.0ms	(pow (sin kx) 2.0)
119.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify4.3s

Counts

113 → 113

Iterations

Useful iterations: 3 (2.2s)

Iter	Nodes	Cost
0	196	68232
1	499	61334
2	1409	60880
3	4448	60840
done	5032	60840

prune971.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 13.0b

localize59.0ms

Local error

Found 4 expressions with local error:

4.5b	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
17.7b	(cbrt (pow (sin kx) 2.0))
17.7b	(cbrt (pow (sin kx) 2.0))
17.7b	(cbrt (pow (sin kx) 2.0))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
2×	`sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 60

Calls

4 calls:

110.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
14.0ms	(cbrt (pow (sin kx) 2.0))
5.0ms	(cbrt (pow (sin kx) 2.0))
5.0ms	(cbrt (pow (sin kx) 2.0))

series1.0s

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (+ (* (* (cbrt (pow (sin kx) 2.0)) (cbrt (pow (sin kx) 2.0))) (cbrt (pow (sin kx) 2.0))) (pow (sin ky) 2.0)))
349.0ms	(cbrt (pow (sin kx) 2.0))
303.0ms	(cbrt (pow (sin kx) 2.0))
282.0ms	(cbrt (pow (sin kx) 2.0))

simplify82.0ms

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	96	47085