Details

sample191.0ms

Algorithm

intervals

Results

148.0ms

256×

body

valid

simplify1.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	2000
5	2000
4	1691
3	564
2	172
1	57
0	22

prune32.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.3b	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
1.5b	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
6.8b	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
12×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `sqr-sin` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

22.0ms	(* (sin ky) (sin ky))
9.0ms	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.0ms	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
5.0ms	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (sin ky) (sin ky))
445.0ms	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
221.0ms	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
376.0ms	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify1.6s

Counts

111 → 111

Iterations

Iter	Nodes
done	2003
4	2003
3	1947
2	766
1	338
0	159

prune969.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize75.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.3b	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1)))
1.5b	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1)
6.8b	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
12×	`pow1`
8×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `associate-/l*`
1×	`pow2` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `div-exp` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `fma-udef` `sqr-sin` `div-inv` `sin-mult` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

20.0ms	(* (sin ky) (sin ky))
8.0ms	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1)))
0.0ms	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1)
2.0ms	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sin ky) (sin ky))
440.0ms	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1)))
228.0ms	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1)
362.0ms	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* 1 (* (sin ky) (sin ky)))) 1))

simplify1.2s

Counts

111 → 111

Iterations

Iter	Nodes
done	2000
3	2000
2	822
1	341
0	160

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize89.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
1.2b	(log (exp (sqrt (fma (/ (* 2 l) Om) (* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))) 1))))
2.6b	(* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))
6.8b	(sqrt (fma (/ (* 2 l) Om) (* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))) 1))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
15×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
10×	`associate-l`
7×	`log-pow`
6×	`exp-prod` `associate-r` `sqrt-prod`
5×	`prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`log-prod` `times-frac` `swap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `fma-udef` `unswap-sqr`
1×	`pow2` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow-plus` `pow1/2` `rem-log-exp` `associate-*l/` `pow-sqr` `pow-prod-up` `sqr-sin` `div-inv` `sin-mult`

Counts

4 → 99

Calls

4 calls:

23.0ms	(* (sin kx) (sin kx))
7.0ms	(log (exp (sqrt (fma (/ (* 2 l) Om) (* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))) 1))))
32.0ms	(* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))
10.0ms	(sqrt (fma (/ (* 2 l) Om) (* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sin kx) (sin kx))
415.0ms	(log (exp (sqrt (fma (/ (* 2 l) Om) (* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))) 1))))
271.0ms	(* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))))
343.0ms	(sqrt (fma (/ (* 2 l) Om) (* (/ (* 2 l) Om) (fma (sin ky) (sin ky) (* (sin kx) (sin kx)))) 1))

simplify1.5s

Counts

111 → 111

Iterations

Iter	Nodes
done	2001
3	2001
2	1300
1	451
0	193

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

localize112.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
1.5b	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
6.8b	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
20.0b	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `fma-udef` `div-inv` `remove-posit16`

Counts

4 → 80

Calls

4 calls:

10.0ms	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.0ms	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
2.0ms	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
1.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))

series1.4s

Counts

4 → 12

Calls

4 calls:

426.0ms	(/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
224.0ms	(fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
301.0ms	(sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
493.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (* 2 l) Om) (/ (* 2 l) Om)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))

simplify1.1s

Counts

92 → 92

Iterations

Iter	Nodes
done	2000
3	2000
2	558
1	224
0	125

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.7b

regimes637.0ms

Accuracy

0% (0.8b remaining)

Error of 1.5b against oracle of 0.8b and baseline of 1.5b

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample4.3s

Algorithm

intervals

Results

4.0s

8000×

body

valid