Details

sample94.0ms

Algorithm

intervals

Results

70.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.5b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
3.5b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
8.5b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

rewrite354.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 127

Calls

4 calls:

10.0ms	(* (sin ky) (sin ky))
121.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
102.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
118.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin ky) (sin ky))
399.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
267.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
447.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

simplify2.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	5008
2	2698
1	691
0	260

prune908.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1)))
0.6b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
3.4b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
8.5b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

rewrite539.0ms

Algorithm

rewrite-expression-head

Rules

91×	`times-frac`
89×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
80×	`associate-r`
77×	`add-cube-cbrt`
32×	`add-cbrt-cube` `add-exp-log`
18×	`distribute-rgt-out` `distribute-lft-out`
16×	`frac-times` `associate-*l/`
15×	`sqrt-prod`
12×	`pow1` `prod-exp` `cbrt-unprod` `sin-mult`
8×	`flip3-+` `flip-+`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r*` `distribute-lft1-in` `count-2` `frac-add` `distribute-rgt1-in`
4×	`sqrt-div` `associate-l` `pow-prod-down` `associate-*r/` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`associate-/r/` `*-commutative` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 203

Calls

4 calls:

142.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1)))
115.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
78.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
199.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

403.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1)))
247.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
213.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
469.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

simplify3.6s

Counts

215 → 215

Iterations

Iter	Nodes
done	5001
2	4689
1	1093
0	346

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize61.0ms

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))
3.4b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
8.5b	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
46.1b	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

rewrite103.0ms

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:

16.0ms	(* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om))
70.0ms	(* (+ (* (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))))

series1.2s

Counts

4 → 12

Calls

4 calls:

265.0ms	(* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om))
221.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
488.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
233.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

simplify2.2s

Counts

163 → 163

Iterations

Iter	Nodes
done	5000
2	3254
1	837
0	279

prune2.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.5b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
3.5b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
8.5b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
21.3b	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-cbrt-cube` `add-exp-log`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
13×	`frac-times`
10×	`pow1`
9×	`prod-exp` `cbrt-unprod`
8×	`sin-mult`
7×	`associate-l/` `associate-r/`
6×	`associate-/r*` `flip3-+` `flip-+`
5×	`cbrt-undiv` `div-exp`
4×	`sqrt-div` `frac-add` `insert-posit16` `add-log-exp`
3×	`associate-l` `pow-prod-down` `associate-/l*`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv` `remove-posit16` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

89.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
88.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
99.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
1.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))))

series1.9s

Counts

4 → 12

Calls

4 calls:

366.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
315.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
886.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))
330.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))))

simplify1.9s

Counts

120 → 120

Iterations

Iter	Nodes
done	5000
2	2111
1	590
0	235

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.5b

regimes562.0ms

Accuracy

0% (0.0b remaining)

Error of 0.6b against oracle of 0.6b and baseline of 0.6b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	30
1	30
0	23

end0.0ms

sample2.6s

Algorithm

intervals

Results

2.3s

8000×

body

valid