Details

sample162.0ms

Algorithm

intervals

Results

132.0ms

256×

body

valid

simplify4.8s

Counts

1 → 1

Iterations

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

prune36.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize53.0ms

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)))
3.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
6.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite460.0ms

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))
160.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
130.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
140.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (sin ky) (sin ky))
355.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
301.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
464.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.3s

Counts

149 → 149

Iterations

Iter	Nodes
2	2975
1	758
0	289

prune2.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize62.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
0.6b	(/ 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))
6.1b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite459.0ms

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:

139.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
135.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
44.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
137.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

246.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
397.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
187.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
390.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.8s

Counts

162 → 162

Iterations

Iter	Nodes
2	3090
1	790
0	290

prune2.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize114.0ms

Local error

Found 4 expressions with local error:

6.1b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

rewrite495.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 67

Calls

4 calls:

170.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
123.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
92.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
109.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

series1.5s

Counts

4 → 12

Calls

4 calls:

494.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
297.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
362.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
344.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

simplify1.5s

Counts

79 → 79

Iterations

Iter	Nodes
3	2574
2	516
1	184
0	95

prune1.8s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

localize107.0ms

Local error

Found 4 expressions with local error:

9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
9.1b	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
8×	`cbrt-div` `sqrt-div`
4×	`pow1` `flip3-+` `add-cbrt-cube` `pow1/3` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`

Counts

4 → 68

Calls

4 calls:

120.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
96.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
111.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
117.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

series1.2s

Counts

4 → 12

Calls

4 calls:

261.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
270.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
348.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
339.0ms	(cbrt (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

simplify1.2s

Counts

80 → 80

Iterations

Iter	Nodes
3	2351
2	486
1	170
0	86

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.5b

regimes680.0ms

Accuracy

0% (0.8b remaining)

Error of 1.5b against oracle of 0.7b and baseline of 1.5b

bsearch0.0ms

simplify25.0ms

Iterations

Iter	Nodes
2	36
1	36
0	27

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.5s

8000×

body

valid