Details

sample346.0ms

Algorithm

intervals

Results

143.0ms	99×	body	1280	valid
87.0ms	49×	body	640	valid
13.0ms	24×	body	320	valid
11.0ms	65×	body	80	valid
11.0ms	19×	body	160	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize27.0ms

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

rewrite198.0ms

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:

115.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
12.0ms	(pow (sin ky) 2.0)
8.0ms	(pow (sin kx) 2.0)
57.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series664.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
125.0ms	(pow (sin ky) 2.0)
186.0ms	(pow (sin kx) 2.0)
124.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.7s

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

prune816.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 8.5b

localize14.0ms

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))

rewrite51.0ms

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))
11.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
38.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

series769.0ms

Counts

3 → 9

Calls

3 calls:

155.0ms	(hypot (sin kx) (sin ky))
264.0ms	(/ (sin ky) (hypot (sin kx) (sin ky)))
351.0ms	(* (/ (sin ky) (hypot (sin kx) (sin ky))) (sin th))

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: 3 (774.0ms)

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

prune446.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.5b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
104×	`add-sqr-sqrt`
92×	`*-un-lft-identity`
90×	`add-cube-cbrt`
44×	`associate-l`
36×	`add-exp-log`
20×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`associate-/l*`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/r/`
1×	`hypot-udef` `pow-flip` `pow-prod-down` `associate-l/` `-commutative` `inv-pow`

Counts

4 → 191

Calls

4 calls:

0.0ms	(hypot (sin kx) (sin ky))
6.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
52.0ms	(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))
16.0ms	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))

series973.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(hypot (sin kx) (sin ky))
254.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
315.0ms	(* (/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky))) (sin th))
215.0ms	(/ 1 (/ (hypot (sin kx) (sin ky)) (sin ky)))

simplify3.2s

Counts

203 → 203

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	255	3365
1	559	2961
2	1260	2616
3	3534	2597
done	5001	2581

prune816.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.5b

localize34.0ms

Local error

Found 3 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`hypot-udef` `associate-/r/`

Counts

3 → 111

Calls

3 calls:

0.0ms	(hypot (sin kx) (sin ky))
6.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
21.0ms	(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))

series892.0ms

Counts

3 → 9

Calls

3 calls:

177.0ms	(hypot (sin kx) (sin ky))
342.0ms	(/ (hypot (sin kx) (sin ky)) (sin ky))
373.0ms	(/ (sin th) (/ (hypot (sin kx) (sin ky)) (sin ky)))

simplify2.9s

Counts

120 → 120

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	192	2165
1	388	2084
2	1198	1943
3	3947	1940
done	5000	1940

prune699.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 8.5b

regimes919.0ms

Accuracy

0% (0.1b remaining)

Error of 9.0b against oracle of 8.8b and baseline of 9.0b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: done (4.0ms)

Iter	Nodes	Cost
0	12	15
1	15	13
done	15	11

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.1s	2718×	body	1280	valid
2.1s	1844×	body	640	valid
765.0ms	752×	body	320	valid
382.0ms	2323×	body	80	valid
175.0ms	363×	body	160	valid