Details

sample466.0ms

Algorithm

intervals

Results

301.0ms	93×	body	1280	valid
49.0ms	56×	body	640	valid
13.0ms	71×	body	80	valid
12.0ms	16×	body	160	valid
11.0ms	20×	body	320	valid

simplify5.2s

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite149.0ms

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:

84.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
4.0ms	(pow (sin ky) 2.0)
43.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
151.0ms	(pow (sin kx) 2.0)
197.0ms	(pow (sin ky) 2.0)
141.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.1s

Counts

129 → 129

Iterations

Useful iterations: 3 (731.0ms)

Iter	Nodes	Cost
0	178	1808
1	340	1625
2	850	1557
3	2640	1556
done	5000	1556

prune754.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.0b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b

(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))

0.2b

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

rewrite50.0ms

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

27.0ms

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

19.0ms

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

series1.6s

Counts

3 → 9

Calls

3 calls:

428.0ms

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

551.0ms

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

637.0ms

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

simplify2.0s

Counts

82 → 82

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	134	1912
1	294	1885
2	797	1670
3	2370	1669
done	5002	1668

prune597.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.2b

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

0.2b

(/ (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:

1.0ms

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

24.0ms

(* (sin ky) (/ (sin th) (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))))

series1.6s

Counts

3 → 9

Calls

3 calls:

419.0ms

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

634.0ms

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

556.0ms

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

simplify2.4s

Counts

82 → 82

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	132	1911
1	287	1871
2	889	1659
3	2812	1659
done	5001	1658

prune501.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
0.2b	(* (sin ky) (/ (sin th) (* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
0.2b	(/ (sin th) (* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
0.5b	(* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
22×	`pow1`
21×	`sqrt-prod`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt` `*-un-lft-identity`
13×	`associate-r`
9×	`sqrt-pow1` `pow1/2` `associate-l`
8×	`swap-sqr`
7×	`times-frac`
6×	`prod-exp` `cbrt-unprod` `unswap-sqr`
5×	`pow-prod-up`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr` `associate-/l*`
2×	`*-commutative` `div-inv`
1×	`pow2` `rem-sqrt-square` `frac-2neg` `pow-plus` `sqrt-unprod` `associate-r/` `clear-num` `associate-/r` `rem-square-sqrt`

Counts

4 → 119

Calls

4 calls:

1.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
42.0ms	(* (sin ky) (/ (sin th) (* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
17.0ms	(/ (sin th) (* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
21.0ms	(* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

464.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
606.0ms	(* (sin ky) (/ (sin th) (* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))))
553.0ms	(/ (sin th) (* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))))
305.0ms	(* (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))

simplify1.6s

Counts

131 → 131

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	169	4476
1	359	2768
2	1177	2366
done	5001	2303

prune574.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.0b

regimes1.2s

Accuracy

0% (0.4b remaining)

Error of 8.9b against oracle of 8.4b and baseline of 8.9b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	35
1	17	35
done	17	35

end0.0ms

sample9.8s

Algorithm

intervals

Results

5.7s	2778×	body	1280	valid
2.0s	1749×	body	640	valid
935.0ms	2289×	body	80	valid
488.0ms	804×	body	320	valid
141.0ms	380×	body	160	valid