Details

sample390.0ms

Algorithm

intervals

Results

197.0ms	91×	body	1280	valid
53.0ms	60×	body	640	valid
14.0ms	72×	body	80	valid
13.0ms	23×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.2s

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	156	16
5	653	16
done	5000	16

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

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))
0.2b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
1.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite195.0ms

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:

120.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
14.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
51.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

233.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
189.0ms	(pow (sin kx) 2.0)
168.0ms	(pow (sin ky) 2.0)
148.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.1s

Counts

130 → 130

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	188	1736
1	462	1637
2	1905	1529
done	5000	1528

prune783.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 9.5b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.2b

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

0.2b

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (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:

0.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

17.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

39.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

series1.5s

Counts

3 → 9

Calls

3 calls:

342.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

572.0ms

(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

567.0ms

(* (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sin th))

simplify1.2s

Counts

82 → 82

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	134	1912
1	311	1885
2	1347	1670
done	5000	1669

prune524.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 9.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
0.2b	(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.2b	(* (expm1 (log1p (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
1.2b	(log1p (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

1.0ms	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
18.0ms	(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
20.0ms	(* (expm1 (log1p (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
1.0ms	(log1p (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

314.0ms	(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))
560.0ms	(/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
462.0ms	(* (expm1 (log1p (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))) (sin th))
478.0ms	(log1p (/ (sin ky) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify599.0ms

Counts

82 → 82

Iterations

Useful iterations: done (595.0ms)

Iter	Nodes	Cost
0	133	1884
1	253	1807
2	877	1597
done	5000	1594

prune533.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 9.5b

localize37.0ms

Local error

Found 3 expressions with local error:

0.1b

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

0.3b

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

0.3b

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite38.0ms

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 (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

9.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

26.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series1.5s

Counts

3 → 9

Calls

3 calls:

386.0ms

(hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))

533.0ms

(/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))

587.0ms

(* (sin ky) (/ (sin th) (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify1.3s

Counts

82 → 82

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	132	1911
1	309	1876
2	1506	1665
done	5001	1659

prune468.0ms

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 9.5b

regimes1.5s

Accuracy

0% (0.3b remaining)

Error of 8.9b against oracle of 8.6b and baseline of 8.9b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	17	21
done	17	21

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.4s	2792×	body	1280	valid
1.6s	1816×	body	640	valid
897.0ms	2351×	body	80	valid
441.0ms	704×	body	320	valid
170.0ms	337×	body	160	valid