Details

sample101.0ms

Algorithm

intervals

Results

80.0ms

256×

body

valid

simplify895.0ms

Counts: 1 → 1

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize77.0ms

Local error

Found 4 expressions with local error:

6.3b	(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)
0.3b	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.2b	(* (sin kx) (sin kx))

rewrite43.0ms

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

23.0ms	(* (sin kx) (sin kx))
10.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
5.0ms	(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)

series975.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

427.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
335.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
191.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
21.0ms	(* (sin kx) (sin kx))

simplify1.0s

Counts: 111 → 111

prune1.9s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.8b

localize52.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.9b	(/ (sin kx) (/ Om l))
2.9b	(/ (sin kx) (/ Om l))
2.7b	(/ (sin ky) (/ Om l))

rewrite55.0ms

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

19.0ms	(/ (sin kx) (/ Om l))
14.0ms	(/ (sin kx) (/ Om l))
14.0ms	(/ (sin ky) (/ Om l))
3.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

328.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
110.0ms	(/ (sin kx) (/ Om l))
86.0ms	(/ (sin kx) (/ Om l))
82.0ms	(/ (sin ky) (/ Om l))

simplify906.0ms

Counts: 247 → 247

prune5.2s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.8b

localize72.0ms

Local error

Found 4 expressions with local error:

18.8b	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
6.3b	(sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.9b	(fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
0.3b	(/ 1/2 (sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

rewrite14.0ms

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:

Slowest

9.0ms	(/ 1/2 (sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
2.0ms	(sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
0.0ms	(fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

series1.4s

Counts

4 → 12

Calls

4 calls:

Slowest

422.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
418.0ms	(/ 1/2 (sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
324.0ms	(sqrt (fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
200.0ms	(fma (* (/ (+ l l) Om) (/ (+ l l) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify2.4s

Counts: 92 → 92

prune3.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

localize99.0ms

Local error

Found 4 expressions with local error:

43.6b	(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))
6.3b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))) (/ (sin kx) (/ Om l)))) 1))
2.9b	(/ (sin kx) (/ Om l))
2.9b	(/ (sin kx) (/ Om l))

rewrite25.0ms

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:

Slowest

10.0ms	(/ (sin kx) (/ Om l))
9.0ms	(/ (sin kx) (/ Om l))
1.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))) (/ (sin kx) (/ Om l)))) 1))
0.0ms	(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))

series645.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

299.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (posit16->real (real->posit16 (/ (sin kx) (/ Om l)))) (/ (sin kx) (/ Om l)))) 1))
124.0ms	(/ (sin kx) (/ Om l))
123.0ms	(/ (sin kx) (/ Om l))
99.0ms	(posit16->real (real->posit16 (/ (sin kx) (/ Om l))))

simplify1.6s

Counts: 185 → 185

prune6.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.8b

regimes485.0ms

Accuracy

0% (0.0b remaining)

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

bsearch9.0ms

end0.0ms

sample4.4s

Algorithm

intervals

Results

4.1s	7999×	body	80	valid
1.0ms	1×	body	160	valid