Details

sample135.0ms

Algorithm

intervals

Results

76.0ms

256×

body

valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5005
4	1812
3	494
2	160
1	57
0	22

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ l l) Om) (/ (+ l l) Om))
0.3b	(* (sin ky) (sin ky))
2.0b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
6.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

rewrite233.0ms

Algorithm

rewrite-expression-head

Rules

188×	`*-un-lft-identity`
184×	`times-frac`
174×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
61×	`swap-sqr`
48×	`distribute-lft-out`
46×	`associate-l`
44×	`associate-r`
42×	`distribute-rgt-out`
36×	`add-cbrt-cube` `add-exp-log`
24×	`pow1`
18×	`distribute-lft1-in` `distribute-rgt1-in`
14×	`frac-times` `prod-exp` `cbrt-unprod`
12×	`count-2`
9×	`sin-mult`
8×	`cbrt-undiv` `div-exp` `associate-l/` `associate-r/`
6×	`unswap-sqr`
5×	`flip3-+` `pow-prod-down` `flip-+`
4×	`frac-add` `insert-posit16` `div-inv` `add-log-exp`
3×	`*-commutative` `sqrt-prod`
2×	`pow2` `pow-plus` `sqrt-div` `pow-sqr` `pow-prod-up`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-sin`

Counts

4 → 252

Calls

4 calls:

29.0ms	(* (/ (+ l l) Om) (/ (+ l l) Om))
10.0ms	(* (sin ky) (sin ky))
73.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
110.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

series853.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (/ (+ l l) Om) (/ (+ l l) Om))
28.0ms	(* (sin ky) (sin ky))
278.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
502.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

simplify3.3s

Counts

264 → 264

Iterations

Iter	Nodes
done	5000
2	4821
1	1319
0	382

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.8b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.6b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
1.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
6.1b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

83×	`associate-r`
78×	`*-un-lft-identity`
74×	`add-sqr-sqrt`
73×	`times-frac`
66×	`add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
19×	`pow1`
18×	`distribute-rgt-out` `distribute-lft-out`
16×	`frac-times` `associate-*l/`
13×	`prod-exp` `cbrt-unprod` `sin-mult`
7×	`flip3-+` `associate-l` `flip-+`
6×	`cbrt-undiv` `distribute-lft1-in` `count-2` `div-exp` `frac-add` `distribute-rgt1-in`
5×	`pow-prod-down`
4×	`associate-*r/` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `*-commutative` `sqrt-prod` `unswap-sqr`
2×	`sqrt-div` `div-inv`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 189

Calls

4 calls:

10.0ms	(* (sin ky) (sin ky))
93.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
63.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
157.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

series961.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sin ky) (sin ky))
298.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
206.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
424.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

simplify1.7s

Counts

201 → 201

Iterations

Iter	Nodes
done	5000
1	1088
0	325

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.8b

localize116.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om))
1.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
6.1b	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
44.9b	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

80×	`associate-r`
75×	`*-un-lft-identity`
74×	`add-sqr-sqrt` `times-frac`
63×	`add-cube-cbrt`
18×	`distribute-rgt-out` `distribute-lft-out`
14×	`add-cbrt-cube` `add-exp-log`
9×	`pow1`
6×	`distribute-lft1-in` `count-2` `associate-l` `distribute-rgt1-in`
4×	`prod-exp` `cbrt-unprod` `insert-posit16` `sin-mult` `add-log-exp` `unswap-sqr`
3×	`frac-times` `flip3-+` `associate-*l/` `sqrt-prod` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `pow-prod-down` `frac-add` `associate-r/` `-commutative` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `remove-posit16`

Counts

4 → 151

Calls

4 calls:

18.0ms	(* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om))
83.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
13.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
0.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

series1.1s

Counts

4 → 12

Calls

4 calls:

239.0ms	(* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om))
201.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
458.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
224.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

simplify2.9s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3254
1	837
0	279

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.8b

localize88.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
2.0b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
6.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
19.8b	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-cbrt-cube` `add-exp-log`
17×	`pow1`
14×	`add-sqr-sqrt`
13×	`frac-times`
10×	`*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
9×	`sin-mult`
7×	`associate-l/` `associate-r/`
6×	`associate-l`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `div-exp` `associate-r` `pow-prod-down` `frac-add` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `sqrt-prod`
2×	`sqrt-div` `*-commutative` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqr-sin` `remove-posit16`

Counts

4 → 94

Calls

4 calls:

12.0ms	(* (sin ky) (sin ky))
90.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
86.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
0.0ms	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))))

series1.2s

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (sin ky) (sin ky))
271.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
443.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
432.0ms	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))))

simplify2.0s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	2283
1	610
0	214

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.8b

regimes630.0ms

Accuracy

0% (0.7b remaining)

Error of 1.4b against oracle of 0.7b and baseline of 1.4b

bsearch1.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	27
1	27
0	20

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.4s

8000×

body

valid