Details

sample112.0ms

Algorithm

intervals

Results

50.0ms	73×	body	1280	valid
32.0ms	75×	body	640	valid
7.0ms	26×	body	320	valid
6.0ms	73×	body	80	valid
2.0ms	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: 13.4b

localize15.0ms

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))
0.3b	(pow (sin kx) 2.0)
0.3b	(pow (sin ky) 2.0)
3.8b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite120.0ms

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:

76.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
3.0ms	(pow (sin kx) 2.0)
3.0ms	(pow (sin ky) 2.0)
33.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series446.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(* (/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin th))
103.0ms	(pow (sin kx) 2.0)
103.0ms	(pow (sin ky) 2.0)
81.0ms	(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	3690	1528
done	5001	1528

prune463.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.3b

localize18.0ms

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))

rewrite29.0ms

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)))

8.0ms

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

series985.0ms

Counts

3 → 9

Calls

3 calls:

253.0ms

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

378.0ms

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

354.0ms

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

simplify1.3s

Counts

82 → 82

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	134	1912
1	294	1885
2	805	1670
3	2383	1669
done	5000	1668

prune339.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.3b

localize15.0ms

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 th) (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)))))

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:

2.0ms

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

8.0ms

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

16.0ms

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

series970.0ms

Counts

3 → 9

Calls

3 calls:

257.0ms

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

337.0ms

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

375.0ms

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

simplify1.4s

Counts

82 → 82

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	132	1911
1	287	1871
2	892	1659
3	2818	1659
done	5000	1658

prune345.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))))
0.2b	(* (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)))))))
0.5b	(* (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)))))

rewrite70.0ms

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))))
15.0ms	(/ (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))))))
38.0ms	(* (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)))))))
12.0ms	(* (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)))))

series1.3s

Counts

4 → 12

Calls

4 calls:

276.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
339.0ms	(/ (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))))))
379.0ms	(* (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)))))))
265.0ms	(* (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)))))

simplify1.0s

Counts

131 → 131

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	169	4476
1	359	2768
2	1175	2366
done	5000	2303

prune364.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 9.3b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 8.9b against oracle of 8.8b and baseline of 8.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	15	19
done	15	19

end0.0ms

sample3.5s

Algorithm

intervals

Results

2.0s	2715×	body	1280	valid
750.0ms	1834×	body	640	valid
225.0ms	792×	body	320	valid
204.0ms	2318×	body	80	valid
60.0ms	341×	body	160	valid