Details

sample454.0ms

Algorithm

intervals

Results

176.0ms	71×	body	80	valid
142.0ms	93×	body	1280	valid
48.0ms	56×	body	640	valid
9.0ms	20×	body	320	valid
8.0ms	16×	body	160	valid

simplify4.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	16
1	23	16
2	35	16
3	64	16
4	136	16
5	311	16
6	1019	16
7	4223	16
done	5001	16

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize45.0ms

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)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
25×	`sqrt-prod`
24×	`times-frac`
16×	`unpow-prod-down`
10×	`distribute-lft-out`
8×	`add-exp-log` `associate-/r*`
7×	`pow1`
6×	`pow-unpow` `add-cbrt-cube`
4×	`sqrt-div` `add-log-exp`
3×	`associate-/l*`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `sqr-pow`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

4 → 100

Calls

4 calls:

59.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
8.0ms	(pow (sin kx) 2.0)
8.0ms	(pow (sin ky) 2.0)
34.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series707.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(/ (sin ky) (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
163.0ms	(pow (sin kx) 2.0)
163.0ms	(pow (sin ky) 2.0)
159.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	170	1738
1	328	1556
2	794	1503
3	2419	1503
done	5000	1503

prune597.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin kx) 2)
0.3b	(pow (sin ky) 2)
0.3b	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
4.4b	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
45×	`sqrt-prod`
41×	`add-sqr-sqrt`
34×	`times-frac`
28×	`add-cube-cbrt`
24×	`associate-l`
18×	`unpow-prod-down`
12×	`distribute-lft-out`
10×	`pow1`
8×	`add-exp-log`
6×	`pow-unpow` `add-cbrt-cube`
4×	`associate-/r/` `add-log-exp` `unswap-sqr`
3×	`rem-sqrt-square` `sqrt-pow1` `associate-r`
2×	`pow-to-exp` `pow-pow` `flip3-+` `sqrt-div` `pow-exp` `flip-+` `div-inv` `unpow2` `sqr-pow`
1×	`pow-flip` `pow1/2` `pow-prod-down` `associate-l/` `prod-exp` `-commutative` `cbrt-unprod` `inv-pow`

Counts

4 → 115

Calls

4 calls:

4.0ms	(pow (sin kx) 2)
4.0ms	(pow (sin ky) 2)
107.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
70.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

series413.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(pow (sin kx) 2)
24.0ms	(pow (sin ky) 2)
196.0ms	(* (sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2)))) (sin ky))
161.0ms	(sqrt (/ 1 (+ (pow (sin kx) 2) (pow (sin ky) 2))))

simplify2.2s

Counts

127 → 127

Iterations

Useful iterations: 3 (886.0ms)

Iter	Nodes	Cost
0	190	1895
1	358	1664
2	794	1563
3	2361	1555
done	5000	1555

prune716.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.7b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
0.4b	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite435.0ms

Algorithm

rewrite-expression-head

Rules

185×	`sqrt-prod`
163×	`add-sqr-sqrt`
144×	`times-frac`
132×	`*-un-lft-identity`
72×	`add-cube-cbrt`
39×	`associate-r` `associate-l`
28×	`add-exp-log` `unswap-sqr`
24×	`unpow-prod-down` `distribute-lft-out`
18×	`add-cbrt-cube`
16×	`sqrt-div`
11×	`associate-/r*`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 225

Calls

4 calls:

281.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
57.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
44.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
37.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series647.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
222.0ms	(/ (sin ky) (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
129.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
113.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify3.2s

Counts

237 → 237

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	259	7250
1	629	6550
2	1810	5634
done	5000	5632

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 10.7b

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
0.3b	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ 1 (/ (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
4.3b	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

rewrite616.0ms

Algorithm

rewrite-expression-head

Rules

428×	`times-frac`
377×	`add-sqr-sqrt`
314×	`sqrt-prod`
279×	`*-un-lft-identity`
152×	`add-cube-cbrt`
116×	`associate-r`
89×	`add-exp-log`
63×	`unswap-sqr`
43×	`div-exp`
39×	`associate-l`
36×	`unpow-prod-down` `distribute-lft-out`
28×	`prod-exp`
27×	`add-cbrt-cube`
15×	`rec-exp` `1-exp`
12×	`sqrt-div`
11×	`associate-/l*`
10×	`pow1` `cbrt-undiv`
6×	`cbrt-unprod` `div-inv`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`pow-prod-down` `associate-/r*` `associate-/r/`
2×	`rem-sqrt-square` `pow-flip` `sqrt-pow1` `pow1/2` `associate-/l/` `inv-pow`
1×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

4 → 362

Calls

4 calls:

74.0ms	(/ (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
395.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ 1 (/ (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))))
42.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
43.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))
234.0ms	(* (/ 1 (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))) (/ 1 (/ (sqrt (sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))) (sin ky))))
110.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
108.0ms	(sqrt (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))

simplify2.8s

Counts

374 → 374

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	438	13435
1	1168	11570
2	2322	10108
done	5000	9914

prune1.4s

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 10.7b

regimes1.4s

Accuracy

68.1% (0.5b remaining)

Error of 11.4b against oracle of 10.9b and baseline of 12.5b

bsearch6.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	59
1	35	59
done	35	59

end0.0ms

sample9.1s

Algorithm

intervals

Results

4.7s	2778×	body	1280	valid
2.2s	1749×	body	640	valid
1.1s	804×	body	320	valid
572.0ms	2289×	body	80	valid
138.0ms	380×	body	160	valid