Details

sample48.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
11.0ms	256×	pre	80	true

simplify843.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	2012
6	2012
5	753
4	228
3	85
2	43
1	18
0	8

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 6.9b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1 (* (/ b a) (/ b a)))
0.4b	(* (/ b a) (/ b a))
6.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity`
32×	`add-cube-cbrt`
15×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod` `insert-posit16`
2×	`difference-of-squares`
1×	`pow2` `frac-times` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow-plus` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `flip--`

Counts

3 → 97

Calls

3 calls:

7.0ms	(- 1 (* (/ b a) (/ b a)))
15.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series88.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(- 1 (* (/ b a) (/ b a)))
27.0ms	(* (/ b a) (/ b a))
13.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify973.0ms

Counts

106 → 106

Iterations

Iter	Nodes
done	2000
3	2000
2	1395
1	473
0	154

prune398.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 6.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (/ (* b (/ b a)) a))
0.2b	(* b (/ b a))
6.0b	(/ (* b (/ b a)) a)
6.9b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
15×	`add-cube-cbrt`
13×	`times-frac` `associate-r`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod` `insert-posit16`
3×	`associate-/r` `associate-l*` `sqrt-prod`
2×	`associate-*r/` `div-inv` `difference-of-squares` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `pow-prod-down` `-commutative` `flip--` `associate-/l` `distribute-lft-out--` `associate-/l/`

Counts

4 → 88

Calls

4 calls:

12.0ms	(- 1 (/ (* b (/ b a)) a))
17.0ms	(* b (/ b a))
10.0ms	(/ (* b (/ b a)) a)
1.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- 1 (/ (* b (/ b a)) a))
31.0ms	(* b (/ b a))
31.0ms	(/ (* b (/ b a)) a)
20.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify953.0ms

Counts

100 → 100

Iterations

Iter	Nodes
done	2013
3	2013
2	1189
1	353
0	141

prune400.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 6.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (/ b a) (/ b a))
0.4b	(* (/ b a) (/ b a))
6.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
6.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`times-frac`
62×	`*-un-lft-identity` `add-cube-cbrt`
28×	`add-cbrt-cube` `add-exp-log`
26×	`swap-sqr` `associate-r` `associate-l`
20×	`pow1`
8×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
6×	`sqrt-prod`
4×	`insert-posit16` `add-log-exp`
2×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 164

Calls

4 calls:

12.0ms	(* (/ b a) (/ b a))
23.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (/ b a) (/ b a))
27.0ms	(* (/ b a) (/ b a))
19.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))
17.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Counts

176 → 176

Iterations

Iter	Nodes
done	2000
3	2000
2	1294
1	401
0	130

prune964.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 6.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (/ b a))
6.0b	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
6.9b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
46.1b	(posit16->real (real->posit16 (* b (/ b a))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-r`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-l` `sqrt-prod` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-r/` `-commutative` `remove-posit16`

Counts

4 → 84

Calls

4 calls:

8.0ms	(* b (/ b a))
4.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
1.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
0.0ms	(posit16->real (real->posit16 (* b (/ b a))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(* b (/ b a))
34.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
19.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
27.0ms	(posit16->real (real->posit16 (* b (/ b a))))

simplify1.4s

Counts

96 → 96

Iterations

Iter	Nodes
done	2006
3	2006
2	842
1	275
0	128

prune776.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 6.8b

regimes152.0ms

Accuracy

0% (0.1b remaining)

Error of 7.5b against oracle of 7.4b and baseline of 7.5b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

934.0ms	8000×	body	80	valid
338.0ms	8000×	pre	80	true