Details

sample349.0ms

Algorithm

intervals

Results

159.0ms	75×	body	1280	valid
60.0ms	65×	body	640	valid
20.0ms	83×	body	80	valid
12.0ms	21×	body	320	valid
4.0ms	12×	body	160	valid

simplify4.9s

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.1b

localize34.0ms

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)
4.0b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite144.0ms

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:

79.0ms	(/ (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)
46.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series669.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
157.0ms	(pow (sin kx) 2.0)
168.0ms	(pow (sin ky) 2.0)
134.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.0s

Counts

129 → 129

Iterations

Useful iterations: 3 (774.0ms)

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

prune743.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 7.0b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b

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

0.1b

(* (/ (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))))

rewrite32.0ms

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)))

20.0ms

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

10.0ms

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

series1.6s

Counts

3 → 9

Calls

3 calls:

420.0ms

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

536.0ms

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

688.0ms

(/ (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

prune577.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 6.9b

localize21.0ms

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)))))

rewrite44.0ms

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)))

16.0ms

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

23.0ms

(* (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:

331.0ms

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

551.0ms

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

599.0ms

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

simplify2.3s

Counts

82 → 82

Iterations

Useful iterations: done (2.3s)

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

prune606.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 6.9b

localize24.0ms

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))))))
0.3b	(/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
0.3b	(/ (/ (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)))))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

526×	`times-frac`
306×	`add-sqr-sqrt`
281×	`add-cube-cbrt` `*-un-lft-identity`
272×	`sqrt-prod`
136×	`associate-r`
25×	`associate-/l*`
20×	`add-exp-log` `add-cbrt-cube`
16×	`div-inv`
12×	`associate-/r*`
7×	`pow1` `cbrt-undiv` `div-exp` `unswap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `-commutative` `associate-/l/`

Counts

4 → 397

Calls

4 calls:

1.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
118.0ms	(* (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))))))
20.0ms	(/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
44.0ms	(/ (/ (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)))))

series2.5s

Counts

4 → 12

Calls

4 calls:

453.0ms	(sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2))))
591.0ms	(* (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))))))
919.0ms	(/ (sin th) (sqrt (hypot (pow (sin kx) (/ 2.0 2)) (pow (sin ky) (/ 2.0 2)))))
497.0ms	(/ (/ (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)))))

simplify2.4s

Counts

409 → 409

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	425	19394
1	995	16487
2	2569	15157
done	5001	14509

prune1.6s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 6.9b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	21
1	20	19
done	20	19

end0.0ms

sample9.2s

Algorithm

intervals

Results

5.0s	2729×	body	1280	valid
2.2s	1786×	body	640	valid
857.0ms	786×	body	320	valid
509.0ms	2350×	body	80	valid
129.0ms	349×	body	160	valid