Details

sample116.0ms

Algorithm

intervals

Results

86.0ms

256×

body

valid

simplify817.0ms

Counts: 1 → 1

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize42.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
2.7b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
0.3b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
0.2b	(* (sin ky) (sin ky))

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-cbrt-cube` `add-exp-log`
29×	`add-sqr-sqrt`
26×	`prod-exp` `cbrt-unprod`
25×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
17×	`pow1`
15×	`sqrt-prod`
13×	`frac-times` `cbrt-undiv` `div-exp`
9×	`sin-mult`
7×	`associate-l/` `associate-r/`
6×	`associate-/r` `flip3-+` `associate-l*` `flip-+`
4×	`sqrt-div` `associate-r` `pow-prod-down` `frac-add` `insert-posit16` `add-log-exp`
3×	`swap-sqr` `associate-/l*`
2×	`associate-/r/` `*-commutative` `unswap-sqr`
1×	`pow2` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow-plus` `pow1/2` `pow-sqr` `pow-prod-up` `sqr-sin` `div-inv`

Counts

4 → 137

Calls

4 calls:

Slowest

129.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
119.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
103.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
11.0ms	(* (sin ky) (sin ky))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

478.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
401.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
315.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
35.0ms	(* (sin ky) (sin ky))

simplify1.6s

Counts: 149 → 149

prune3.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize57.0ms

Local error

Found 4 expressions with local error:

6.3b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
2.5b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
0.6b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
0.3b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
28×	`add-sqr-sqrt`
25×	`*-un-lft-identity` `add-cube-cbrt`
24×	`times-frac`
17×	`cbrt-undiv` `div-exp`
16×	`frac-times` `associate-*l/`
15×	`sqrt-prod`
14×	`associate-r`
12×	`pow1` `sin-mult`
8×	`flip3-+` `flip-+`
6×	`associate-/r*` `frac-add`
4×	`sqrt-div` `associate-l` `pow-prod-down` `associate-*r/` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`associate-/r/` `*-commutative`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `unswap-sqr`

Counts

4 → 150

Calls

4 calls:

Slowest

165.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
152.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
94.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
56.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))

series1.3s

Counts

4 → 12

Calls

4 calls:

Slowest

477.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
371.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
293.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
202.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))

simplify1.6s

Counts: 162 → 162

prune2.9s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.8b

localize61.0ms

Local error

Found 4 expressions with local error:

36.1b	(posit16->real (real->posit16 (* (sin ky) (sin ky))))
6.3b	(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
2.7b	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
0.3b	(/ 1/2 (sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-cbrt-cube` `add-exp-log`
25×	`prod-exp` `cbrt-unprod`
23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
13×	`cbrt-undiv` `div-exp`
10×	`pow1`
9×	`frac-times`
6×	`associate-/r` `flip3-+` `associate-r/` `flip-+`
5×	`associate-*l/`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`associate-l` `pow-prod-down` `associate-/l*`
2×	`associate-/r/`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv` `remove-posit16` `unswap-sqr`

Counts

4 → 114

Calls

4 calls:

Slowest

168.0ms	(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
133.0ms	(/ 1/2 (sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
93.0ms	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
0.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

477.0ms	(sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
355.0ms	(/ 1/2 (sqrt (+ (* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
253.0ms	(* (+ (posit16->real (real->posit16 (* (sin ky) (sin ky)))) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
22.0ms	(posit16->real (real->posit16 (* (sin ky) (sin ky))))

simplify1.3s

Counts: 126 → 126

prune3.6s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.8b

localize89.0ms

Local error

Found 4 expressions with local error:

17.8b	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
6.3b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
2.7b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
0.3b	(/ 1/2 (posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))

rewrite299.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-cbrt-cube` `add-exp-log`
25×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`frac-times` `cbrt-undiv` `div-exp`
10×	`pow1`
9×	`times-frac`
8×	`sin-mult`
7×	`associate-l/` `associate-r/`
5×	`flip3-+` `flip-+`
4×	`frac-add` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-l` `pow-prod-down` `sqrt-prod` `associate-/l`
2×	`sqrt-div`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `div-inv` `remove-posit16` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

Slowest

172.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
113.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
9.0ms	(/ 1/2 (posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
1.0ms	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))

series1.6s

Counts

4 → 12

Calls

4 calls:

Slowest

445.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
407.0ms	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
393.0ms	(/ 1/2 (posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
324.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))

simplify1.2s

Counts: 116 → 116

prune3.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.8b

regimes777.0ms

Accuracy

0% (0.6b remaining)

Error of 1.4b against oracle of 0.7b and baseline of 1.4b

bsearch10.0ms

end0.0ms

sample3.9s

Algorithm

intervals

Results

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