Details

sample368.0ms

Algorithm

intervals

Results

132.0ms	83×	body	1280	valid
117.0ms	60×	body	640	valid
17.0ms	78×	body	80	valid
14.0ms	23×	body	320	valid
5.0ms	12×	body	160	valid

simplify5.0s

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: 12.0b

localize43.0ms

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))
0.3b	(pow (sin ky) 2.0)
0.3b	(pow (sin kx) 2.0)
3.7b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite213.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
30×	`associate-l`
26×	`times-frac`
25×	`add-cube-cbrt`
21×	`sqrt-prod`
20×	`unpow-prod-down`
11×	`add-exp-log`
9×	`pow1` `add-cbrt-cube` `hypot-def`
8×	`distribute-lft-out` `sqr-pow`
6×	`pow-unpow`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `unswap-sqr`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+`
1×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

4 → 118

Calls

4 calls:

135.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
4.0ms	(pow (sin ky) 2.0)
4.0ms	(pow (sin kx) 2.0)
65.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series737.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
164.0ms	(pow (sin ky) 2.0)
204.0ms	(pow (sin kx) 2.0)
144.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.9s

Counts

130 → 130

Iterations

Useful iterations: 3 (1.2s)

Iter	Nodes	Cost
0	188	1736
1	403	1637
2	1070	1529
3	3697	1528
done	5000	1528

prune887.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.1b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite58.0ms

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 kx) (sin ky))
18.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
34.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

series825.0ms

Counts

3 → 9

Calls

3 calls:

203.0ms	(hypot (sin kx) (sin ky))
289.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
332.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: 3 (759.0ms)

Iter	Nodes	Cost
0	130	1126
1	284	1107
2	790	987
3	2322	984
done	5000	984

prune509.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.1b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite49.0ms

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 kx) (sin ky))
17.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
28.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

series832.0ms

Counts

3 → 9

Calls

3 calls:

183.0ms	(hypot (sin kx) (sin ky))
289.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
360.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

simplify2.1s

Counts

82 → 82

Iterations

Useful iterations: 3 (774.0ms)

Iter	Nodes	Cost
0	121	1123
1	253	1092
2	786	976
3	2466	975
done	5000	975

prune543.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.1b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite53.0ms

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 kx) (sin ky))
18.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
32.0ms	(* (sin ky) (* 1 (/ (sin th) (hypot (sin kx) (sin ky)))))

series851.0ms

Counts

3 → 9

Calls

3 calls:

162.0ms	(hypot (sin kx) (sin ky))
324.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
365.0ms	(* (sin ky) (* 1 (/ (sin th) (hypot (sin kx) (sin ky)))))

simplify3.4s

Counts

73 → 73

Iterations

Useful iterations: 3 (696.0ms)

Iter	Nodes	Cost
0	128	1053
1	253	965
2	645	826
3	1726	825
done	5000	825

prune290.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.1b

regimes1.0s

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.7b and baseline of 8.9b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (2.0ms)

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

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.8s	2745×	body	1280	valid
2.3s	1867×	body	640	valid
896.0ms	756×	body	320	valid
423.0ms	2251×	body	80	valid
201.0ms	381×	body	160	valid