Details

sample144.0ms

Algorithm

intervals

Results

106.0ms

256×

body

valid

simplify4.5s

Counts

1 → 1

Iterations

Iter	Nodes
5	7210
4	1654
3	464
2	156
1	57
0	22

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
0.3b	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
1.8b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite466.0ms

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:

22.0ms	(* (sin kx) (sin kx))
181.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
127.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
129.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (sin kx) (sin kx))
404.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
265.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
559.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.6s

Counts

149 → 149

Iterations

Iter	Nodes
2	3214
1	759
0	290

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin kx) (sin kx))
1.0b	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
1.8b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite631.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

22.0ms	(* (sin kx) (sin kx))
278.0ms	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
136.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
191.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

28.0ms	(* (sin kx) (sin kx))
474.0ms	(log (exp (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))
302.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
460.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
2	3018
1	703
0	261

prune2.5s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.6b

localize84.0ms

Local error

Found 4 expressions with local error:

1.0b	(log (exp (sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))))) 1))))
1.8b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.0b	(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))))) 1))
28.6b	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-cbrt-cube` `add-exp-log`
25×	`prod-exp` `cbrt-unprod`
13×	`frac-times` `*-un-lft-identity`
12×	`cbrt-undiv` `div-exp`
11×	`add-sqr-sqrt` `pow1`
9×	`add-cube-cbrt`
8×	`log-pow` `sqrt-prod` `sin-mult`
7×	`exp-prod` `associate-l/` `associate-r/`
5×	`flip3-+` `flip-+`
4×	`frac-add` `insert-posit16` `add-log-exp`
3×	`log-prod` `associate-l` `pow-prod-down`
2×	`sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `associate-r` `*-commutative` `remove-posit16` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

10.0ms	(log (exp (sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))))) 1))))
87.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
5.0ms	(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))))) 1))
0.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

469.0ms	(log (exp (sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))))) 1))))
273.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
458.0ms	(sqrt (+ (posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))))) 1))
262.0ms	(posit16->real (real->posit16 (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
2	2603
1	621
0	234

prune3.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

localize68.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1/2 (posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
1.8b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
8.0b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
23.8b	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))

rewrite305.0ms

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:

4.0ms	(/ 1/2 (posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
125.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
174.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
0.0ms	(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:

366.0ms	(/ 1/2 (posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))))
270.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
504.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))
462.0ms	(posit16->real (real->posit16 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))))

simplify1.6s

Counts

116 → 116

Iterations

Iter	Nodes
2	2723
1	663
0	251

prune4.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.6b

regimes454.0ms

Accuracy

0% (0.8b remaining)

Error of 1.6b against oracle of 0.8b and baseline of 1.6b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	28
1	28
0	21

end0.0ms

sample3.8s

Algorithm

intervals

Results

3.5s

8000×

body

valid