Details

sample127.0ms

Algorithm

intervals

Results

91.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize47.0ms

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)))
2.5b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
8.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

rewrite554.0ms

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:

25.0ms	(* (sin ky) (sin ky))
203.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
166.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
150.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

24.0ms	(* (sin ky) (sin ky))
462.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1)))
245.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om)))
562.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (+ l l) Om) (/ (+ l l) Om))) 1))

simplify2.4s

Counts

139 → 139

Iterations

Iter	Nodes
done	5008
2	2698
1	691
0	260

prune993.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize75.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
0.5b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1)))
3.4b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
8.0b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

rewrite741.0ms

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:

163.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
193.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1)))
114.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
262.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

290.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om))
418.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1)))
196.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
423.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)) (/ (+ l l) Om)) 1))

simplify3.9s

Counts

215 → 215

Iterations

Iter	Nodes
done	5004
2	4464
1	1096
0	346

prune1.6s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

localize97.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1/2 (sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1)))
3.4b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
8.0b	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
46.0b	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt` `*-un-lft-identity` `times-frac`
49×	`add-cube-cbrt`
40×	`associate-r`
15×	`sqrt-prod`
11×	`add-cbrt-cube` `add-exp-log`
9×	`distribute-rgt-out` `distribute-lft-out`
7×	`pow1`
6×	`associate-/r*`
4×	`flip3-+` `sqrt-div` `flip-+` `insert-posit16` `sin-mult` `add-log-exp`
3×	`frac-times` `distribute-lft1-in` `count-2` `associate-l` `associate-l/` `distribute-rgt1-in` `associate-/l`
2×	`cbrt-undiv` `div-exp` `frac-add` `prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `remove-posit16`

Counts

4 → 133

Calls

4 calls:

39.0ms	(/ 1/2 (sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1)))
84.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
30.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
1.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

series1.4s

Counts

4 → 12

Calls

4 calls:

452.0ms	(/ 1/2 (sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1)))
214.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))
514.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
204.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

simplify2.2s

Counts

145 → 145

Iterations

Iter	Nodes
done	5001
2	2365
1	695
0	269

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize95.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
8.0b	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
46.0b	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))
46.0b	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `remove-posit16`

Counts

4 → 50

Calls

4 calls:

23.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
33.0ms	(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))))
0.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

series1.4s

Counts

4 → 12

Calls

4 calls:

490.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
542.0ms	(sqrt (+ (* (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om)))) (/ (+ l l) Om)) 1))
173.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))
219.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (+ l l) Om))))

simplify2.8s

Counts

62 → 62

Iterations

Iter	Nodes
done	5005
3	2480
2	547
1	166
0	79

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes633.0ms

Accuracy

13.3% (4.7b remaining)

Error of 5.4b against oracle of 0.7b and baseline of 6.2b

bsearch404.0ms

Steps

Iters	Range		Point
7	3.069771180936197e+216	5.5712605373046926e+218	1.5365535845369674e+218
9	-2.042479401704603e+109	-6.465553349696891e+100	-1.537064068705883e+108

simplify33.0ms

Iterations

Iter	Nodes
done	70
1	70
0	54

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.5s

8000×

body

valid