Details

sample117.0ms

Algorithm

intervals

Results

89.0ms

256×

body

valid

simplify803.0ms

Counts: 1 → 1

prune38.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.2b

localize51.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.9b	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.5b	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b	(* (sin kx) (sin kx))

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:

Slowest

21.0ms	(* (sin kx) (sin kx))
9.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
6.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
0.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series958.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

447.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
283.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
207.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
20.0ms	(* (sin kx) (sin kx))

simplify868.0ms

Counts: 111 → 111

prune2.1s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize90.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
3.2b	(/ (sin kx) (/ Om l))
3.2b	(/ (sin kx) (/ Om l))
2.7b	(/ (sin ky) (/ Om l))

rewrite70.0ms

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:

Slowest

20.0ms	(/ (sin ky) (/ Om l))
20.0ms	(/ (sin kx) (/ Om l))
19.0ms	(/ (sin kx) (/ Om l))
3.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series627.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

339.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
105.0ms	(/ (sin kx) (/ Om l))
99.0ms	(/ (sin kx) (/ Om l))
84.0ms	(/ (sin ky) (/ Om l))

simplify953.0ms

Counts: 247 → 247

prune5.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize125.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
6.0b	(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))

rewrite11.0ms

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:

Slowest

3.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

459.0ms	(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
326.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
320.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
308.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify1.5s

Counts: 77 → 77

prune1.7s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.9b

localize114.0ms

Local error

Found 4 expressions with local error:

9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
9.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
6.0b	(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))

rewrite11.0ms

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:

Slowest

3.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
2.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

375.0ms	(cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
357.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
320.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
308.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify1.4s

Counts: 77 → 77

prune2.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.9b

regimes501.0ms

Accuracy

0% (0.0b remaining)

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

bsearch13.0ms

end0.0ms

sample3.7s

Algorithm

intervals

Results

3.4s

8000×

body

valid