Details

sample171.0ms

Algorithm

intervals

Results

112.0ms

256×

body

valid

simplify255.0ms

Calls

1 calls:

Slowest

254.0ms

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

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.4b

localize40.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
1.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b	(* (sin kx) (sin kx))
0.2b	(* (* l (/ 2 Om)) (* l (/ 2 Om)))

rewrite2.5s

Algorithm

rewrite-expression-head

Rules

1278×	`associate-*r/`
1034×	`frac-times`
502×	`add-sqr-sqrt`
480×	`associate-/l*`
479×	`*-un-lft-identity`
360×	`associate-/r*`
323×	`add-cube-cbrt`
289×	`sin-mult`
240×	`clear-num` `un-div-inv`
238×	`associate-r`
145×	`flip3-+` `flip-+`
144×	`frac-add`
120×	`frac-2neg`
100×	`times-frac`
99×	`unswap-sqr`
98×	`associate-l`
89×	`add-cbrt-cube` `add-exp-log`
69×	`pow1`
58×	`swap-sqr` `associate-*l/`
53×	`prod-exp` `cbrt-unprod`
31×	`pow-prod-down`
15×	`distribute-lft-out`
13×	`*-commutative`
12×	`cbrt-undiv` `div-exp`
9×	`sqrt-prod`
8×	`div-inv`
5×	`pow-sqr` `pow-prod-up`
4×	`insert-posit16` `add-log-exp`
3×	`pow-plus`
2×	`pow2` `sqrt-div`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sqr-sin`

Calls

4 calls:

Slowest

1.8s	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
474.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
124.0ms	(* (* l (/ 2 Om)) (* l (/ 2 Om)))
21.0ms	(* (sin kx) (sin kx))

series1.2s

Calls

4 calls:

Slowest

869.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
252.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
64.0ms	(* (* l (/ 2 Om)) (* l (/ 2 Om)))
33.0ms	(* (sin kx) (sin kx))

simplify6.0m

Calls

1602 calls:

Slowest

1.2s	(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l (/ 2 Om)) (* l (/ 2 Om))) (* l (/ 2 Om)))))
1.2s	(* (* 2 2) (* (/ Om 2) (/ Om 2)))
1.2s	(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))
1.1s	(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l l) l) (* (* (/ 2 Om) (/ 2 Om)) (/ 2 Om)))))
1.1s	(* (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx)))) (* (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om))) (* (* (* l l) l) (/ (* (* 2 2) 2) (* (* Om Om) Om)))))

prune19.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize77.0ms

Local error

Found 4 expressions with local error:

6.8b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
1.9b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
0.3b	(* (sin kx) (sin kx))
0.3b	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))

rewrite5.8s

Algorithm

rewrite-expression-head

Rules

1051×	`associate-*r/`
913×	`frac-times`
386×	`*-un-lft-identity`
384×	`associate-/l*`
365×	`add-sqr-sqrt`
289×	`sin-mult`
288×	`associate-/r*`
242×	`add-cube-cbrt`
192×	`clear-num` `un-div-inv`
163×	`associate-r`
145×	`flip3-+` `flip-+`
144×	`frac-add`
96×	`frac-2neg`
70×	`associate-l` `unswap-sqr`
54×	`times-frac` `add-exp-log`
53×	`add-cbrt-cube`
47×	`associate-*l/`
33×	`swap-sqr`
32×	`prod-exp` `cbrt-unprod`
31×	`pow1`
25×	`distribute-lft-out`
18×	`sqrt-prod`
14×	`pow-prod-down`
13×	`log-pow`
12×	`exp-prod`
8×	`*-commutative`
6×	`cbrt-undiv` `div-exp`
4×	`insert-posit16` `div-inv` `add-log-exp`
3×	`log-prod`
2×	`sqrt-div` `rem-log-exp`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqr-sin`

Calls

4 calls:

Slowest

3.5s	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
1.8s	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
465.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
11.0ms	(* (sin kx) (sin kx))

series1.3s

Calls

4 calls:

Slowest

513.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))
475.0ms	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om)))) 1))))
290.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (* l (/ 2 Om)) (* l (/ 2 Om))))
38.0ms	(* (sin kx) (sin kx))