Details

sample214.0ms

Algorithm

intervals

Results

181.0ms

256×

body

valid

simplify4.7s

Counts

1 → 1

Iterations

Iter	Nodes
5	7482
4	1754
3	519
2	162
1	55
0	22

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.9b

localize59.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin kx) (sin kx))
0.4b	(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
2.9b	(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
9.1b	(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

rewrite30.0ms

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 kx) (sin kx))
5.0ms	(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.0ms	(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
3.0ms	(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

series1.1s

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (sin kx) (sin kx))
480.0ms	(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
200.0ms	(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
344.0ms	(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify1.1s

Counts

111 → 111

Iterations

Iter	Nodes
3	2245
2	759
1	315
0	159

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize56.0ms

Local error

Found 4 expressions with local error:

2.4b	(/ (sin kx) (/ Om l))
4.9b	(/ l (/ Om (sin ky)))
4.9b	(/ l (/ Om (sin ky)))
9.1b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

225×	`times-frac`
132×	`add-sqr-sqrt`
131×	`*-un-lft-identity` `add-cube-cbrt`
39×	`associate-/r*`
19×	`add-cbrt-cube` `add-exp-log`
15×	`div-inv`
9×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-/r/` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 235

Calls

4 calls:

29.0ms	(/ (sin kx) (/ Om l))
17.0ms	(/ l (/ Om (sin ky)))
9.0ms	(/ l (/ Om (sin ky)))
1.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series680.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ (sin kx) (/ Om l))
120.0ms	(/ l (/ Om (sin ky)))
123.0ms	(/ l (/ Om (sin ky)))
361.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify1.1s

Counts

247 → 247

Iterations

Iter	Nodes
2	2353
1	801
0	330

prune5.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize84.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ l (/ Om (sin ky)))
4.9b	(/ l (/ Om (sin ky)))
9.1b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky)))))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
48.5b	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
90×	`add-sqr-sqrt`
89×	`*-un-lft-identity` `add-cube-cbrt`
26×	`associate-/r*`
14×	`add-cbrt-cube` `add-exp-log`
10×	`div-inv`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod`
2×	`clear-num` `frac-2neg` `associate-/r/`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `remove-posit16`

Counts

4 → 173

Calls

4 calls:

8.0ms	(/ l (/ Om (sin ky)))
10.0ms	(/ l (/ Om (sin ky)))
1.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky)))))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
0.0ms	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(/ l (/ Om (sin ky)))
100.0ms	(/ l (/ Om (sin ky)))
262.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (posit16->real (real->posit16 (/ l (/ Om (sin ky)))))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
95.0ms	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

simplify2.5s

Counts

185 → 185

Iterations

Iter	Nodes
3	3993
2	1259
1	459
0	208

prune6.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize83.0ms

Local error

Found 4 expressions with local error:

4.9b	(/ l (/ Om (sin ky)))
9.1b	(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ l (/ Om (sin ky))))) (posit16->real (real->posit16 (/ l (/ Om (sin ky)))))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
48.5b	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))
48.5b	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity` `add-cube-cbrt`
13×	`associate-/r*`
9×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `sqrt-prod` `associate-/l*`
2×	`remove-posit16`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-/r/`

Counts

4 → 111

Calls

4 calls:

8.0ms	(/ l (/ Om (sin ky)))
1.0ms	(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ l (/ Om (sin ky))))) (posit16->real (real->posit16 (/ l (/ Om (sin ky)))))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
0.0ms	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))
0.0ms	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

series723.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ l (/ Om (sin ky)))
377.0ms	(sqrt (fma 4 (+ (* (posit16->real (real->posit16 (/ l (/ Om (sin ky))))) (posit16->real (real->posit16 (/ l (/ Om (sin ky)))))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
115.0ms	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))
133.0ms	(posit16->real (real->posit16 (/ l (/ Om (sin ky)))))

simplify2.9s

Counts

123 → 123

Iterations

Iter	Nodes
3	4161
2	1291
1	456
0	207

prune5.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

regimes600.0ms

Accuracy

0% (1.5b remaining)

Error of 2.2b against oracle of 0.6b and baseline of 2.2b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
2	27
1	27
0	25

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.7s

8000×

body

valid