Details

sample159.0ms

Algorithm

intervals

Results

128.0ms

256×

body

valid

simplify4.0s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.6b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
2.7b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite534.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
26×	`prod-exp` `cbrt-unprod`
25×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
17×	`pow1`
15×	`sqrt-prod`
13×	`frac-times` `cbrt-undiv` `div-exp`
9×	`sin-mult`
7×	`associate-l/` `associate-r/`
6×	`associate-/r` `flip3-+` `associate-l*` `flip-+`
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 → 137

Calls

4 calls:

22.0ms	(* (sin ky) (sin ky))
159.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
134.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
213.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

26.0ms	(* (sin ky) (sin ky))
393.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
274.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
542.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.6s

Counts

149 → 149

Iterations

Iter	Nodes
2	2975
1	758
0	289

prune2.9s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
2.2b	(log (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
2.7b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite861.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-cbrt-cube` `add-exp-log`
37×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity` `add-cube-cbrt`
25×	`prod-exp` `log-pow` `cbrt-unprod`
24×	`exp-prod` `sqrt-prod`
13×	`frac-times` `cbrt-undiv` `div-exp`
11×	`pow1`
8×	`sin-mult`
7×	`flip3-+` `associate-l/` `associate-r/` `flip-+`
6×	`associate-/r*` `sqrt-div`
4×	`frac-add` `associate-/r/` `insert-posit16` `add-log-exp`
3×	`log-prod` `associate-l` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `rem-log-exp` `associate-r` `*-commutative` `unswap-sqr`

Counts

4 → 146

Calls

4 calls:

207.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
347.0ms	(log (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
129.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
174.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

355.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
411.0ms	(log (exp (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
282.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
425.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.8s

Counts

158 → 158

Iterations

Iter	Nodes
2	2884
1	733
0	313

prune3.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.7b	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
2.7b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite618.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

21.0ms	(* (sin ky) (sin ky))
299.0ms	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
103.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
190.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (sin ky) (sin ky))
396.0ms	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
279.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
493.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
2	2997
1	703
0	260

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize105.0ms

Local error

Found 4 expressions with local error:

0.7b	(log (exp (sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
2.7b	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.0b	(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
34.4b	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

255.0ms	(log (exp (sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
112.0ms	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
142.0ms	(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
1.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

series1.3s

Counts

4 → 12

Calls

4 calls:

495.0ms	(log (exp (sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
272.0ms	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
497.0ms	(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
25.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

simplify1.1s

Counts

103 → 103

Iterations

Iter	Nodes
2	2588
1	559
0	223

prune2.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

regimes628.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	28
1	28
0	23

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.5s

8000×

body

valid