Details

sample297.0ms

Algorithm

intervals

Results

109.0ms	91×	body	1280	valid
60.0ms	28×	body	320	valid
40.0ms	58×	body	640	valid
9.0ms	64×	body	80	valid
4.0ms	15×	body	160	valid

simplify11.5s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	13	16
1	28	16
2	75	16
3	272	16
done	5001	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.8b

localize20.0ms

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)))

rewrite110.0ms

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:

58.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
4.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
39.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series633.0ms

Counts

4 → 12

Calls

4 calls:

202.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
152.0ms	(pow (sin kx) 2.0)
138.0ms	(pow (sin ky) 2.0)
141.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify5.4s

Counts

129 → 129

Iterations

Useful iterations: done (5.4s)

Iter	Nodes	Cost
0	178	1808
1	1203	1619
done	5000	1559

prune782.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 7.2b

localize14.0ms

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)))

rewrite61.0ms

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))
40.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
16.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

series860.0ms

Counts

3 → 9

Calls

3 calls:

198.0ms	(hypot (sin ky) (sin kx))
394.0ms	(* (/ (sin ky) (hypot (sin ky) (sin kx))) (sin th))
267.0ms	(/ (sin ky) (hypot (sin ky) (sin kx)))

simplify5.5s

Counts

82 → 82

Iterations

Useful iterations: done (5.5s)

Iter	Nodes	Cost
0	130	1126
1	1457	1106
done	5000	987

prune476.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.2b

localize28.0ms

Local error

Found 3 expressions with local error:

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

rewrite62.0ms

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))
39.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
17.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

series853.0ms

Counts

3 → 9

Calls

3 calls:

185.0ms	(hypot (sin kx) (sin ky))
427.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))
241.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))

simplify5.9s

Counts

82 → 82

Iterations

Useful iterations: done (5.9s)

Iter	Nodes	Cost
0	130	1126
1	1457	1107
done	5001	987

prune420.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 7.2b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite29.0ms

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))
18.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
9.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))

series874.0ms

Counts

3 → 9

Calls

3 calls:

204.0ms	(hypot (sin kx) (sin ky))
360.0ms	(* (sin ky) (/ (sin th) (hypot (sin kx) (sin ky))))
310.0ms	(/ (sin th) (hypot (sin kx) (sin ky)))

simplify8.8s

Counts

82 → 82

Iterations

Useful iterations: done (8.8s)

Iter	Nodes	Cost
0	121	1123
1	1360	1092
done	5001	976

prune339.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 7.2b

regimes785.0ms

Accuracy

0% (0.1b remaining)

Error of 8.7b against oracle of 8.5b and baseline of 8.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	10	11
done	10	11

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.2s	2751×	body	1280	valid
2.8s	1789×	body	640	valid
968.0ms	2310×	body	80	valid
483.0ms	806×	body	320	valid
225.0ms	344×	body	160	valid