Details

sample165.0ms

Algorithm

intervals

Results

135.0ms

256×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
5	2008
4	1812
3	494
2	160
1	57
0	22

prune28.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin ky) (sin ky))
0.4b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
3.5b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
7.3b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite514.0ms

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:

24.0ms	(* (sin ky) (sin ky))
173.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
125.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
187.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sin ky) (sin ky))
357.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
286.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
455.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.2s

Counts

149 → 149

Iterations

Iter	Nodes
done	2001
2	2001
1	786
0	289

prune2.8s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize507.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
1.1b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
2.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
7.3b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite545.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`times-frac`
17×	`cbrt-undiv` `div-exp`
16×	`frac-times` `associate-*l/`
15×	`sqrt-prod`
14×	`associate-r`
12×	`pow1` `sin-mult`
8×	`flip3-+` `flip-+`
6×	`associate-/r*` `frac-add`
4×	`sqrt-div` `associate-l` `pow-prod-down` `associate-*r/` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `unswap-sqr`

Counts

4 → 150

Calls

4 calls:

155.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
131.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
64.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
192.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

379.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
261.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
161.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
475.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.3s

Counts

162 → 162

Iterations

Iter	Nodes
done	2001
2	2001
1	809
0	290

prune3.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.4b

localize79.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
6.6b	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
7.3b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
7.3b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite697.0ms

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:

157.0ms	(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)))
192.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
159.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

298.0ms	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
305.0ms	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
489.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
375.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.2s

Counts

88 → 88

Iterations

Iter	Nodes
done	2013
3	2013
2	577
1	194
0	98

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.4b

localize93.0ms

Local error

Found 4 expressions with local error:

2.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
6.6b	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
7.3b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
7.3b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite613.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

45.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
184.0ms	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
137.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
245.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.4s

Counts

4 → 12

Calls

4 calls:

213.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
338.0ms	(sqrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
404.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
468.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.4s

Counts

100 → 100

Iterations

Iter	Nodes
done	2000
3	2000
2	1824
1	504
0	203

prune2.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 1.4b

regimes629.0ms

Accuracy

0% (0.8b remaining)

Error of 1.4b against oracle of 0.6b and baseline of 1.4b

bsearch0.0ms

simplify16.0ms

Iterations

Iter	Nodes
done	31
1	31
0	23

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.5s	7999×	body	80	valid
1.0ms	1×	body	160	valid