Details

sample181.0ms

Algorithm

intervals

Results

103.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

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

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize79.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin kx) (sin kx))
0.4b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
2.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.6b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite524.0ms

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:

15.0ms	(* (sin kx) (sin kx))
203.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
123.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
177.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (sin kx) (sin kx))
380.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
305.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
502.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.3s

Counts

149 → 149

Iterations

Iter	Nodes
done	2000
2	2000
1	791
0	290

prune1.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
0.4b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
3.3b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
9.6b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite567.0ms

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:

168.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
201.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
46.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
147.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

269.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
386.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
181.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
481.0ms	(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	2002
2	2002
1	807
0	290

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.9b

localize138.0ms

Local error

Found 4 expressions with local error:

7.6b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
9.6b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
9.6b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
9.6b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite658.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`sqrt-div`
7×	`pow1`
6×	`cbrt-prod`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

118.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
172.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
128.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
239.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.8s

Counts

4 → 12

Calls

4 calls:

323.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
451.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
537.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
452.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.2s

Counts

77 → 77

Iterations

Iter	Nodes
done	2002
3	2002
2	517
1	186
0	95

prune895.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.9b

localize86.0ms

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)))
3.3b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
3.5b	(log (exp (/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))))
9.6b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite870.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 129

Calls

4 calls:

154.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
76.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
473.0ms	(log (exp (/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))))
164.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

413.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
193.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
374.0ms	(log (exp (/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))))
512.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.7s

Counts

141 → 141

Iterations

Iter	Nodes
done	2000
3	2000
2	1939
1	592
0	274

prune1.2s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.9b

regimes658.0ms

Accuracy

0% (0.7b remaining)

Error of 1.3b against oracle of 0.6b and baseline of 1.3b

bsearch0.0ms

simplify14.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.8s

8000×

body

valid