Details

sample286.0ms

Algorithm

intervals

Results

250.0ms

256×

body

valid

simplify4.0s

Counts

1 → 1

Iterations

Iter	Nodes
5	7036
4	1661
3	470
2	154
1	55
0	22

prune35.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (sin ky))
0.3b	(* (sin kx) (sin kx))
2.1b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.2b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite353.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

22.0ms	(* (sin ky) (sin ky))
16.0ms	(* (sin kx) (sin kx))
114.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
196.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series821.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin ky) (sin ky))
35.0ms	(* (sin kx) (sin kx))
274.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
476.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.4s

Counts

135 → 135

Iterations

Iter	Nodes
2	3260
1	762
0	264

prune2.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize79.0ms

Local error

Found 4 expressions with local error:

7.4b	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
7.4b	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
8.2b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
8.2b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite725.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

209.0ms	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
188.0ms	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
148.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
178.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.6s

Counts

4 → 12

Calls

4 calls:

326.0ms	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
373.0ms	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
458.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
455.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
3	2374
2	511
1	192
0	98

prune1.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize120.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
7.4b	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
8.2b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
8.2b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite682.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-cbrt-cube` `add-exp-log`
25×	`prod-exp` `cbrt-unprod`
16×	`sqrt-prod`
14×	`add-sqr-sqrt`
13×	`frac-times` `pow1`
12×	`cbrt-undiv` `div-exp`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div` `sin-mult`
7×	`flip3-+` `associate-l/` `associate-r/` `flip-+`
6×	`sqrt-pow1`
4×	`rem-sqrt-square` `pow1/2` `frac-add` `insert-posit16` `add-log-exp`
3×	`associate-l` `pow-prod-down`
1×	`associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 105

Calls

4 calls:

134.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
175.0ms	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
181.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
189.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
325.0ms	(sqrt (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
464.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
487.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.5s

Counts

117 → 117

Iterations

Iter	Nodes
2	2779
1	639
0	242

prune3.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
2.1b	(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.2b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
35.3b	(posit16->real (real->posit16 (* (sin kx) (sin kx))))

rewrite300.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-cbrt-cube` `add-exp-log`
26×	`prod-exp` `cbrt-unprod`
17×	`pow1`
14×	`add-sqr-sqrt`
12×	`cbrt-undiv` `div-exp`
10×	`*-un-lft-identity` `add-cube-cbrt`
9×	`frac-times`
6×	`associate-l` `associate-*r/`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`associate-r` `pow-prod-down` `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` `sin-mult`

Counts

4 → 100

Calls

4 calls:

11.0ms	(* (sin kx) (sin kx))
112.0ms	(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
174.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
1.0ms	(posit16->real (real->posit16 (* (sin kx) (sin kx))))

series797.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (sin kx) (sin kx))
277.0ms	(* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
456.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (posit16->real (real->posit16 (* (sin kx) (sin kx))))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
32.0ms	(posit16->real (real->posit16 (* (sin kx) (sin kx))))

simplify1.0s

Counts

112 → 112

Iterations

Iter	Nodes
2	2834
1	613
0	230

prune3.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes563.0ms

Accuracy

0% (1.0b remaining)

Error of 1.9b against oracle of 1.0b and baseline of 1.9b

bsearch0.0ms

simplify17.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.8s

8000×

body

valid