Details

sample199.0ms

Algorithm

intervals

Results

108.0ms

256×

body

valid

simplify4.3s

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.8b

localize69.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.3b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
2.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.5b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite503.0ms

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:

11.0ms	(* (sin ky) (sin ky))
190.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
140.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
158.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.2s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin ky) (sin ky))
369.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
322.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
504.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.4s

Counts

149 → 149

Iterations

Iter	Nodes
2	2975
1	758
0	289

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize61.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.3b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
2.5b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
8.5b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite408.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
17×	`add-cbrt-cube` `add-exp-log`
15×	`sqrt-prod`
14×	`pow1`
10×	`associate-r`
6×	`associate-/r` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `sin-mult`
4×	`flip3-+` `sqrt-div` `flip-+` `insert-posit16` `add-log-exp`
3×	`frac-times` `cbrt-undiv` `swap-sqr` `div-exp` `associate-l/` `associate-/l`
2×	`pow-prod-down` `frac-add` `associate-/r/` `*-commutative` `div-inv` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `associate-*r/` `pow-sqr` `pow-prod-up` `sqr-sin`

Counts

4 → 120

Calls

4 calls:

11.0ms	(* (sin ky) (sin ky))
165.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
60.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
170.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (sin ky) (sin ky))
395.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
245.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
439.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify8.9s

Counts

132 → 132

Iterations

Iter	Nodes
3	8015
2	1925
1	611
0	251

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1/2 (sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
2.5b	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om))
8.5b	(sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
33.5b	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

rewrite306.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
23×	`*-un-lft-identity` `add-cube-cbrt`
21×	`times-frac`
15×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
7×	`pow1` `associate-r`
6×	`associate-/r*`
4×	`flip3-+` `sqrt-div` `prod-exp` `cbrt-unprod` `flip-+` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `associate-/l*`
2×	`frac-times` `associate-*l/` `associate-/r/` `div-inv`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `remove-posit16` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

122.0ms	(/ 1/2 (sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
39.0ms	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* 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))
0.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

series1.0s

Counts

4 → 12

Calls

4 calls:

368.0ms	(/ 1/2 (sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
223.0ms	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om))
423.0ms	(sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
32.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

simplify6.9s

Counts

111 → 111

Iterations

Iter	Nodes
3	7522
2	1658
1	500
0	218

prune2.6s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize137.0ms

Local error

Found 4 expressions with local error:

8.5b	(sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
33.5b	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
33.5b	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
33.5b	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

137.0ms	(sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
0.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
0.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
0.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

series526.0ms

Counts

4 → 12

Calls

4 calls:

455.0ms	(sqrt (+ (* (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
30.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
20.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
21.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

simplify1.2s

Counts

55 → 55

Iterations

Iter	Nodes
3	2445
2	469
1	155
0	75

prune1.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes631.0ms

Accuracy

0% (1.4b remaining)

Error of 2.1b against oracle of 0.8b and baseline of 2.1b

bsearch0.0ms

simplify12.0ms

Iterations

Iter	Nodes
2	32
1	32
0	26

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.7s

8000×

body

valid