Details

sample143.0ms

Algorithm

intervals

Results

110.0ms

256×

body

valid

simplify4.7s

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.0b

localize49.0ms

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)))
2.5b	(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
7.3b	(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

rewrite39.0ms

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:

29.0ms	(* (sin kx) (sin kx))
4.0ms	(/ 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))

series944.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (sin kx) (sin kx))
415.0ms	(/ 1/2 (sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
189.0ms	(fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
304.0ms	(sqrt (fma (* (/ l (/ Om 2)) (/ l (/ Om 2))) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

simplify1.3s

Counts

111 → 111

Iterations

Iter	Nodes
3	2245
2	759
1	315
0	159

prune867.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.2b

localize49.0ms

Local error

Found 4 expressions with local error:

2.8b	(/ (sin kx) (/ Om l))
2.9b	(/ l (/ Om (sin ky)))
2.9b	(/ l (/ Om (sin ky)))
7.3b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

rewrite35.0ms

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:

15.0ms	(/ (sin kx) (/ Om l))
7.0ms	(/ l (/ Om (sin ky)))
8.0ms	(/ 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))

series587.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (sin kx) (/ Om l))
98.0ms	(/ l (/ Om (sin ky)))
98.0ms	(/ l (/ Om (sin ky)))
278.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify1.2s

Counts

247 → 247

Iterations

Iter	Nodes
2	2353
1	801
0	330

prune2.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.2b

localize92.0ms

Local error

Found 4 expressions with local error:

6.6b	(sqrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
6.6b	(sqrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
7.3b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
7.3b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

26×	`sqrt-prod`
16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt`
6×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

2.0ms	(sqrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
2.0ms	(sqrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
1.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
1.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

446.0ms	(sqrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
438.0ms	(sqrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
290.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
333.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify1.9s

Counts

88 → 88

Iterations

Iter	Nodes
4	2723
3	913
2	347
1	154
0	83

prune806.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 1.2b

localize134.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
7.3b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
7.3b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
7.3b	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow1`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

2.0ms	(cbrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
2.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

475.0ms	(cbrt (sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
309.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
342.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
357.0ms	(sqrt (fma 4 (+ (* (/ l (/ Om (sin ky))) (/ l (/ Om (sin ky)))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify2.1s

Counts

77 → 77

Iterations

Iter	Nodes
4	2795
3	894
2	332
1	147
0	80

prune1.2s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 1.2b

regimes799.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
2	25
1	25
0	23

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.5s	7999×	body	80	valid
1.0ms	1×	body	160	valid