Details

sample148.0ms

Algorithm

intervals

Results

92.0ms

256×

body

valid

simplify8.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
5	4017
4	920
3	263
2	121
1	52
0	22

prune33.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize194.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (sin ky) 2.0)
0.5b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
2.5b	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite184.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
21×	`times-frac`
19×	`add-exp-log`
15×	`sqrt-prod`
13×	`unpow-prod-down`
11×	`associate-l`
8×	`add-cbrt-cube`
6×	`pow1` `associate-/r*` `prod-exp`
5×	`associate-r`
4×	`sqrt-div` `pow-exp` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `flip3-+` `div-exp` `flip-+` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out`
1×	`distribute-rgt-in` `cbrt-undiv` `rem-sqrt-square` `clear-num` `pow-pow` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod`

Counts

4 → 114

Calls

4 calls:

5.0ms	(pow (sin ky) 2.0)
14.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
135.0ms	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
19.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series3.8s

Counts

4 → 12

Calls

4 calls:

249.0ms	(pow (sin ky) 2.0)
1.4s	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))
1.0s	(* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.2s	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) 2.0) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify4.0s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	1835
1	586
0	226

prune2.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.6b

localize157.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
0.5b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
3.4b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

rewrite450.0ms

Algorithm

rewrite-expression-head

Rules

125×	`add-exp-log`
72×	`prod-exp`
36×	`pow-exp`
33×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`div-exp`
24×	`times-frac`
22×	`associate-l`
17×	`unpow-prod-down`
15×	`sqrt-prod`
13×	`add-cbrt-cube`
12×	`pow-to-exp`
6×	`associate-/r` `associate-r` `associate-r/`
5×	`distribute-rgt-in` `pow1` `distribute-lft-in`
4×	`flip3-+` `sqrt-div` `cbrt-unprod` `flip-+` `insert-posit16` `add-log-exp`
3×	`div-inv` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`associate-/r/` `*-commutative` `distribute-lft-out`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2`

Counts

4 → 155

Calls

4 calls:

168.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
28.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
225.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
15.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

series4.7s

Counts

4 → 12

Calls

4 calls:

987.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))
1.6s	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))
1.1s	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.1s	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))

simplify5.1s

Counts

167 → 167

Iterations

Iter	Nodes
done	5003
2	2145
1	664
0	250

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize165.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
3.4b	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
8.0b	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
46.0b	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
24×	`add-cube-cbrt`
21×	`times-frac`
18×	`add-exp-log`
15×	`sqrt-prod`
11×	`associate-l`
10×	`unpow-prod-down`
8×	`add-cbrt-cube`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `associate-r`
4×	`sqrt-div` `insert-posit16` `add-log-exp`
3×	`flip3-+` `div-exp` `pow-exp` `flip-+` `associate-/l*` `unswap-sqr`
2×	`associate-*r/` `associate-/r/` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `*-commutative` `cbrt-unprod` `remove-posit16`

Counts

4 → 105

Calls

4 calls:

19.0ms	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
148.0ms	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
11.0ms	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
1.0ms	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series5.1s

Counts

4 → 12

Calls

4 calls:

1.5s	(/ 1.0 (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
1.2s	(* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))
1.3s	(sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0))))))))
1.1s	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify4.1s

Counts

117 → 117

Iterations

Iter	Nodes
done	5000
2	1564
1	510
0	204

prune2.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.6b

localize458.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
46.0b	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
46.0b	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
46.0b	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `add-log-exp`
3×	`sqrt-prod` `remove-posit16`
2×	`cbrt-div` `sqrt-div`
1×	`flip3-+` `pow1/3` `flip-+`

Counts

4 → 44

Calls

4 calls:

6.0ms	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
1.0ms	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.0ms	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.0ms	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

series4.6s

Counts

4 → 12

Calls

4 calls:

1.2s	(cbrt (sqrt (+ 1.0 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))))))
1.3s	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
984.0ms	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))
1.2s	(posit16->real (real->posit16 (* (pow (/ (* 2.0 l) Om) (/ 2.0 2)) (+ (pow (sin kx) 2.0) (pow (sin ky) 2.0)))))

simplify6.0s

Counts

56 → 56

Iterations

Iter	Nodes
done	5003
3	2555
2	511
1	168
0	84

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.6b

regimes3.7s

Accuracy

0% (0.8b remaining)

Error of 1.5b against oracle of 0.7b and baseline of 1.5b

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample2.7s

Algorithm

intervals

Results

2.2s

8000×

body

valid