Details

sample126.0ms

Algorithm

intervals

Results

99.0ms

256×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1691
3	564
2	172
1	57
0	22

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.0b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.5b	(/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
2.1b	(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
8.0b	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite28.0ms

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:

13.0ms	(* (sin ky) (sin ky))
6.0ms	(/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
0.0ms	(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
4.0ms	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series975.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (sin ky) (sin ky))
462.0ms	(/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))
164.0ms	(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
326.0ms	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify2.4s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
3	2034
2	753
1	325
0	153

prune757.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize63.0ms

Local error

Found 4 expressions with local error:

7.5b	(sqrt (/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
7.5b	(sqrt (/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
8.0b	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
8.0b	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

70×	`sqrt-prod`
44×	`add-sqr-sqrt`
40×	`times-frac`
32×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `rem-sqrt-square`
4×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-div` `div-inv`

Counts

4 → 108

Calls

4 calls:

7.0ms	(sqrt (/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
6.0ms	(sqrt (/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
1.0ms	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
2.0ms	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

series1.4s

Counts

4 → 12

Calls

4 calls:

365.0ms	(sqrt (/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
426.0ms	(sqrt (/ 1/2 (sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
264.0ms	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))
297.0ms	(sqrt (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))

simplify2.7s

Counts

120 → 120

Iterations

Iter	Nodes
done	5003
4	3281
3	874
2	321
1	174
0	118

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize84.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1/2 (sqrt (posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
2.1b	(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
8.0b	(sqrt (posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
11.0b	(posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))

rewrite30.0ms

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:

22.0ms	(/ 1/2 (sqrt (posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
1.0ms	(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
3.0ms	(sqrt (posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
1.0ms	(posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))

series1.1s

Counts

4 → 12

Calls

4 calls:

460.0ms	(/ 1/2 (sqrt (posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))))
175.0ms	(fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)
305.0ms	(sqrt (posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1))))
180.0ms	(posit16->real (real->posit16 (fma (* (* (/ 2 Om) l) (* (/ 2 Om) l)) (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) 1)))

simplify2.0s

Counts

92 → 92

Iterations

Iter	Nodes
done	5000
3	1966
2	522
1	215
0	119

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin ky) (sin ky))
0.5b	(/ 1/2 (sqrt (fma (* (/ 2 Om) l) (* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l)) 1)))
3.4b	(* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l))
8.0b	(sqrt (fma (* (/ 2 Om) l) (* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l)) 1))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

26.0ms	(* (sin ky) (sin ky))
11.0ms	(/ 1/2 (sqrt (fma (* (/ 2 Om) l) (* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l)) 1)))
48.0ms	(* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l))
3.0ms	(sqrt (fma (* (/ 2 Om) l) (* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l)) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (sin ky) (sin ky))
430.0ms	(/ 1/2 (sqrt (fma (* (/ 2 Om) l) (* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l)) 1)))
343.0ms	(* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l))
333.0ms	(sqrt (fma (* (/ 2 Om) l) (* (fma (sin kx) (sin kx) (* (sin ky) (sin ky))) (* (/ 2 Om) l)) 1))

simplify1.6s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1248
1	439
0	194

prune952.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.6b

regimes580.0ms

Accuracy

46.1% (3.6b remaining)

Error of 4.3b against oracle of 0.7b and baseline of 7.4b

bsearch450.0ms

Steps

Iters	Range		Point
9	5.732452695341516e+179	1.1169139070730355e+189	6.514983512121752e+179
9	-2.042479401704603e+109	-6.465553349696891e+100	-8.522909308188593e+103

simplify22.0ms

Iterations

Iter	Nodes
done	51
1	51
0	39

end0.0ms

sample2.8s

Algorithm

intervals

Results

2.5s

8000×

body

valid