Details

sample607.0ms

Algorithm

intervals

Results

581.0ms

256×

body

valid

simplify172.0ms

Calls

1 calls:

Slowest

171.0ms

(sqrt (* (/ 1 2) (+ 1 (/ 1 (sqrt (+ 1 (* (pow (/ (* 2 l) Om) 2) (+ (pow (sin kx) 2) (pow (sin ky) 2)))))))))

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize70.0ms

Local error

Found 4 expressions with local error:

8.0b	(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)
0.3b	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
0.3b	(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`fma-udef`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `pow1/2` `div-inv`

Calls

4 calls:

Slowest

4.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
1.0ms	(/ 1/2 (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)
0.0ms	(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

series819.0ms

Calls

4 calls:

Slowest

342.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
258.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
147.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)
72.0ms	(fma (sin ky) (sin ky) (* (sin kx) (sin kx)))

simplify3.3s

Calls

22 calls:

Slowest

343.0ms	(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
313.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
307.0ms	(sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
306.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
305.0ms	(cbrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

prune1.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize40.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
2.8b	(/ (sin kx) (/ Om l))
2.8b	(/ (sin kx) (/ Om l))
2.4b	(/ (sin ky) (/ Om l))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
33×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `add-cube-cbrt`
15×	`div-inv`
12×	`associate-/r*`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/l*`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `associate-/r/` `sqrt-prod`
1×	`rem-sqrt-square` `pow1/2`

Calls

4 calls:

Slowest

4.0ms	(/ (sin kx) (/ Om l))
4.0ms	(/ (sin ky) (/ Om l))
4.0ms	(/ (sin kx) (/ Om l))
1.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

series508.0ms

Calls

4 calls:

Slowest

244.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
96.0ms	(/ (sin kx) (/ Om l))
94.0ms	(/ (sin ky) (/ Om l))
74.0ms	(/ (sin kx) (/ Om l))

simplify3.9s

Calls

112 calls:

Slowest

371.0ms	(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
353.0ms	(/ (* (* (sin kx) (sin kx)) (sin kx)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
353.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
352.0ms	(/ (* (* (sin ky) (sin ky)) (sin ky)) (* (* (/ Om l) (/ Om l)) (/ Om l)))
298.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

prune2.4s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
8.3b	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
8.0b	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
8.0b	(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

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

Calls

4 calls:

Slowest

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

series1.2s

Calls

4 calls:

Slowest

380.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
340.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
240.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))
225.0ms	(sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))

simplify6.0s

Calls

36 calls:

Slowest

373.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
371.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))
367.0ms	(sqrt (sqrt (* (cbrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)) (cbrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
360.0ms	(sqrt (* (cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1))) (cbrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))))
339.0ms	(sqrt (sqrt (fma 4 (+ (* (/ (sin ky) (/ Om l)) (/ (sin ky) (/ Om l))) (* (/ (sin kx) (/ Om l)) (/ (sin kx) (/ Om l)))) 1)))

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

22.1b	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
8.0b	(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)
0.3b	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-/r*` `sqrt-prod`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `pow1/2` `fma-udef` `div-inv` `remove-posit16`

Calls

4 calls:

Slowest

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

series901.0ms

Calls

4 calls:

Slowest

304.0ms	(/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
267.0ms	(posit16->real (real->posit16 (/ 1/2 (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))))
213.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
117.0ms	(fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)

simplify3.3s

Calls

22 calls:

Slowest

364.0ms	(sqrt (* (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)) (cbrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))))
351.0ms	(sqrt (sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1)))
345.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
332.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))
293.0ms	(sqrt (fma (* (/ (* l 2) Om) (/ (* l 2) Om)) (fma (sin ky) (sin ky) (* (sin kx) (sin kx))) 1))

prune2.0s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.2b

regimes360.0ms

Accuracy

0% (0.0b remaining)

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

bsearch13.0ms

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.7s

8000×

body

valid