Details

sample167.0ms

Algorithm

intervals

Results

97.0ms

256×

body

valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	2008
5	2008
4	1812
3	494
2	160
1	57
0	22

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 1.2b

localize68.0ms

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)))
2.1b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
6.8b	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

rewrite476.0ms

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:

23.0ms	(* (sin kx) (sin kx))
114.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
152.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
178.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

series1.3s

Counts

4 → 12

Calls

4 calls:

35.0ms	(* (sin kx) (sin kx))
473.0ms	(/ 1/2 (sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1)))
299.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om)))
484.0ms	(sqrt (+ (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (* (/ (* l 2) Om) (/ (* l 2) Om))) 1))

simplify1.9s

Counts

149 → 149

Iterations

Iter	Nodes
done	2000
2	2000
1	791
0	290

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize86.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
0.6b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
2.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
6.8b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite645.0ms

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:

180.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
171.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
86.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
203.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

462.0ms	(/ 1/2 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1)))
301.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
220.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
539.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.4s

Counts

162 → 162

Iterations

Iter	Nodes
done	2001
2	2001
1	809
0	290

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
1.2b	(log (exp (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))
2.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
6.8b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

rewrite699.0ms

Algorithm

rewrite-expression-head

Rules

67×	`add-cbrt-cube` `add-exp-log`
32×	`prod-exp` `cbrt-unprod`
16×	`add-sqr-sqrt` `frac-times` `cbrt-undiv` `div-exp` `associate-*l/`
14×	`associate-r`
13×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
12×	`sin-mult`
7×	`flip3-+` `log-pow` `flip-+`
6×	`exp-prod` `times-frac` `frac-add` `sqrt-prod`
4×	`associate-l` `pow-prod-down` `associate-*r/` `insert-posit16` `add-log-exp`
3×	`log-prod`
2×	`sqrt-div` `*-commutative` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `unswap-sqr`

Counts

4 → 127

Calls

4 calls:

147.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
274.0ms	(log (exp (sqrt (+ (* (* (+ (* (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))
189.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

series1.5s

Counts

4 → 12

Calls

4 calls:

322.0ms	(* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om))
489.0ms	(log (exp (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))
245.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
474.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))

simplify1.3s

Counts

139 → 139

Iterations

Iter	Nodes
done	2002
2	2002
1	750
0	260

prune1.3s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.7b

localize104.0ms

Local error

Found 4 expressions with local error:

1.2b	(log (exp (posit16->real (real->posit16 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))))
2.6b	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
6.8b	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
19.3b	(posit16->real (real->posit16 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))

rewrite301.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

2.0ms	(log (exp (posit16->real (real->posit16 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))))
83.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
214.0ms	(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))))

series1.7s

Counts

4 → 12

Calls

4 calls:

444.0ms	(log (exp (posit16->real (real->posit16 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))))
225.0ms	(* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om))
499.0ms	(sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))
533.0ms	(posit16->real (real->posit16 (sqrt (+ (* (* (+ (* (sin ky) (sin ky)) (* (sin kx) (sin kx))) (/ (* l 2) Om)) (/ (* l 2) Om)) 1))))

simplify1.9s

Counts

87 → 87

Iterations

Iter	Nodes
done	2006
3	2006
2	1734
1	476
0	191

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.7b

regimes543.0ms

Accuracy

0% (0.2b remaining)

Error of 1.2b against oracle of 1.0b and baseline of 1.2b

bsearch0.0ms

simplify15.0ms

Iterations

Iter	Nodes
done	33
1	33
0	25

end0.0ms

sample4.3s

Algorithm

intervals

Results

3.9s

8000×

body

valid