Details

sample178.0ms

Algorithm

intervals

Results

147.0ms

256×

body

valid

simplify4.2s

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: 1.9b

localize81.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.4b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
3.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite549.0ms

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))
190.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
133.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
196.0ms	(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))
365.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
296.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
520.0ms	(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

prune2.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize86.0ms

Local error

Found 4 expressions with local error:

5.6b	(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
9.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
9.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
9.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite546.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
23×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
8×	`sqrt-div`
7×	`pow1`
4×	`flip3-+` `add-cbrt-cube` `add-exp-log` `flip-+` `insert-posit16` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 82

Calls

4 calls:

95.0ms	(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
141.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
168.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
139.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.9s

Counts

4 → 12

Calls

4 calls:

477.0ms	(cbrt (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
443.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
462.0ms	(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))

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
3	2575
2	610
1	267
0	157

prune2.6s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize61.0ms

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)))
3.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
24.3b	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

rewrite481.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

175.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
157.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
147.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
0.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

349.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
273.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
430.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
410.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

simplify1.5s

Counts

130 → 130

Iterations

Iter	Nodes
2	2802
1	663
0	264

prune3.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize81.0ms

Local error

Found 4 expressions with local error:

3.6b	(log (exp (posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))))
3.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.1b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
24.3b	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

rewrite268.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

4.0ms	(log (exp (posit16->real (real->posit16 (/ 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)))
135.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
0.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

397.0ms	(log (exp (posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))))
263.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
462.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
367.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

simplify1.4s

Counts

104 → 104

Iterations

Iter	Nodes
2	2591
1	601
0	234

prune3.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

regimes515.0ms

Accuracy

0% (1.0b remaining)

Error of 1.7b against oracle of 0.7b and baseline of 1.7b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	30
1	30
0	24

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.7s

8000×

body

valid