Details

sample128.0ms

Algorithm

intervals

Results

98.0ms

256×

body

valid

simplify1.5s

Counts: 1 → 1

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.7b

localize97.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.2b	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.4b	(/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b	(* (sin kx) (sin kx))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 174

Calls

4 calls:

Slowest

16.0ms	(/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
14.0ms	(* (sin kx) (sin kx))
5.0ms	(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)

series1.0s

Counts

4 → 12

Calls

4 calls:

Slowest

439.0ms	(/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
342.0ms	(sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
229.0ms	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
21.0ms	(* (sin kx) (sin kx))

simplify1.3s

Counts: 186 → 186

prune4.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize97.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.2b	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.7b	(/ (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (/ 1 2)))
0.4b	(/ (sqrt (/ 1 2)) (/ (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (/ 1 2))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

5243×	`times-frac`
3613×	`sqrt-prod`
2289×	`add-sqr-sqrt`
2288×	`*-un-lft-identity` `add-cube-cbrt`
230×	`div-inv`
117×	`associate-/r*`
22×	`associate-/l*`
19×	`sqrt-div` `associate-/r/`
11×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-undiv`
2×	`clear-num` `frac-2neg`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef` `associate-/l/`

Counts

4 → 1915

Calls

4 calls:

Slowest

12.0ms	(/ (sqrt (/ 1 2)) (/ (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (/ 1 2))))
6.0ms	(/ (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (/ 1 2)))
1.0ms	(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)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

538.0ms	(/ (sqrt (/ 1 2)) (/ (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (/ 1 2))))
413.0ms	(/ (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (sqrt (/ 1 2)))
291.0ms	(sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
177.0ms	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify6.5s

Counts: 1927 → 1927

prune55.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize115.0ms

Local error

Found 4 expressions with local error:

9.4b	(sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
2.3b	(log (exp (/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
2.2b	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.4b	(/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

273×	`times-frac`
153×	`add-sqr-sqrt`
152×	`*-un-lft-identity` `add-cube-cbrt`
84×	`sqrt-prod`
83×	`log-pow`
82×	`exp-prod`
15×	`div-inv`
13×	`add-exp-log` `associate-/l*`
9×	`add-cbrt-cube`
6×	`pow1` `associate-/r*` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `log-prod`
1×	`rem-sqrt-square` `rec-exp` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `rem-log-exp` `fma-udef` `associate-/l/`

Counts

4 → 241

Calls

4 calls:

Slowest

15.0ms	(/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
10.0ms	(log (exp (/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
1.0ms	(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)

series1.7s

Counts

4 → 12

Calls

4 calls:

Slowest

639.0ms	(sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
465.0ms	(log (exp (/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
445.0ms	(/ (/ 1 2) (sqrt (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
190.0ms	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify1.2s

Counts: 253 → 253

prune6.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize110.0ms

Local error

Found 4 expressions with local error:

2.2b	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.5b	(/ (sqrt (log (exp (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) (sqrt (/ 1 2)))
0.5b	(log (exp (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b	(* (sin kx) (sin kx))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

262×	`sqrt-prod`
259×	`times-frac`
151×	`add-sqr-sqrt`
149×	`*-un-lft-identity` `add-cube-cbrt`
72×	`log-pow`
54×	`exp-prod`
29×	`pow1`
16×	`associate-/r*`
12×	`div-inv`
10×	`associate-/l*`
8×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `log-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l`
2×	`fma-udef`
1×	`pow2` `cbrt-undiv` `sqrt-undiv` `clear-num` `frac-2neg` `pow-plus` `sqrt-div` `div-exp` `rem-log-exp` `exp-sum` `pow-prod-down` `prod-exp` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqr-sin` `sin-mult` `unswap-sqr`

Counts

4 → 263

Calls

4 calls:

Slowest

16.0ms	(* (sin kx) (sin kx))
9.0ms	(/ (sqrt (log (exp (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) (sqrt (/ 1 2)))
2.0ms	(log (exp (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)

series849.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

445.0ms	(/ (sqrt (log (exp (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))) (sqrt (/ 1 2)))
190.0ms	(fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
184.0ms	(log (exp (fma (* (* (/ l Om) 2) (* (/ l Om) 2)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
30.0ms	(* (sin kx) (sin kx))

simplify983.0ms

Counts: 275 → 275

prune7.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.6b

regimes752.0ms

Accuracy

0% (1.0b remaining)

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

bsearch7.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

3.6s	7999×	body	80	valid
1.0ms	1×	body	160	valid