Details

sample107.0ms

Algorithm

intervals

Results

58.0ms	85×	body	1280	valid
17.0ms	46×	body	640	valid
8.0ms	31×	body	320	valid
7.0ms	85×	body	80	valid
1.0ms	9×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
0.2b	(pow (sin ky) 2.0)
0.2b	(pow (sin kx) 2.0)
3.5b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite119.0ms

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:

80.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin ky) 2.0)
3.0ms	(pow (sin kx) 2.0)
28.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

160.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
104.0ms	(pow (sin ky) 2.0)
110.0ms	(pow (sin kx) 2.0)
79.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.7s

Counts

130 → 130

Iterations

Useful iterations: 3 (750.0ms)

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

prune481.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin kx) (sin ky))
0.1b	(/ (sin ky) (hypot (sin kx) (sin ky)))
0.1b	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

rewrite28.0ms

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 kx) (sin ky))
8.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
18.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

series531.0ms

Counts

3 → 9

Calls

3 calls:

119.0ms	(hypot (sin kx) (sin ky))
174.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
238.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: 3 (475.0ms)

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

prune282.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.3b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin kx) (sin ky))
0.2b	(/ (sin th) (hypot (sin kx) (sin ky)))
0.2b	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

rewrite27.0ms

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 kx) (sin ky))
8.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
16.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

series560.0ms

Counts

3 → 9

Calls

3 calls:

123.0ms	(hypot (sin kx) (sin ky))
208.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))
229.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: 3 (539.0ms)

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

prune297.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 9.3b

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot (sin kx) (sin ky))
0.2b	(/ (sin th) (* 1 (hypot (sin kx) (sin ky))))
0.2b	(* (sin ky) (/ (sin th) (* 1 (hypot (sin kx) (sin ky)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

0.0ms	(hypot (sin kx) (sin ky))
11.0ms	(/ (sin th) (* 1 (hypot (sin kx) (sin ky))))
27.0ms	(* (sin ky) (/ (sin th) (* 1 (hypot (sin kx) (sin ky)))))

series564.0ms

Counts

3 → 9

Calls

3 calls:

120.0ms	(hypot (sin kx) (sin ky))
212.0ms	(/ (sin th) (* 1 (hypot (sin kx) (sin ky))))
233.0ms	(* (sin ky) (/ (sin th) (* 1 (hypot (sin kx) (sin ky)))))

simplify1.5s

Counts

73 → 73

Iterations

Useful iterations: 3 (569.0ms)

Iter	Nodes	Cost
0	120	1057
1	249	899
2	710	746
3	2274	745
done	5000	745

prune184.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.3b

regimes552.0ms

Accuracy

0% (0.2b remaining)

Error of 9.1b against oracle of 8.9b and baseline of 9.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	12	13
done	12	13

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.9s	2696×	body	1280	valid
967.0ms	1742×	body	640	valid
223.0ms	791×	body	320	valid
216.0ms	2396×	body	80	valid
79.0ms	375×	body	160	valid