Details

sample47.0ms

Algorithm

intervals

Results

26.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify911.0ms

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: 4.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
4.6b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
40×	`times-frac`
31×	`*-un-lft-identity` `add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
10×	`pow1`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
3×	`sqrt-prod`
2×	`insert-posit16` `add-log-exp`
1×	`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

2 → 82

Calls

2 calls:

14.0ms	(* (/ b a) (/ b a))
1.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series53.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(* (/ b a) (/ b a))
13.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify1.2s

Counts

88 → 88

Iterations

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

prune831.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 4.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (/ b a) b)
4.6b	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
7.0b	(/ (* (/ b a) b) a)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`times-frac` `associate-l`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-r*` `sqrt-prod` `insert-posit16` `add-log-exp`
2×	`associate-*l/` `div-inv` `unswap-sqr`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-prod-down` `-commutative` `associate-/l` `associate-/l/`

Counts

3 → 72

Calls

3 calls:

13.0ms	(* (/ b a) b)
1.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
12.0ms	(/ (* (/ b a) b) a)

series85.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* (/ b a) b)
17.0ms	(sqrt (fabs (- 1 (/ (* (/ b a) b) a))))
41.0ms	(/ (* (/ b a) b) a)

simplify922.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	2089
3	2089
2	874
1	266
0	111

prune759.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
0.0b	(exp (* (/ b a) (/ b a)))
0.4b	(* (/ b a) (/ b a))
5.4b	(log (exp (* (/ b a) (/ b a))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`pow1` `swap-sqr` `associate-r` `associate-l`
7×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `div-inv` `unswap-sqr`
3×	`log-prod` `log-pow` `sqrt-prod`
2×	`exp-prod` `exp-to-pow`
1×	`pow2` `frac-times` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `rem-log-exp` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `rem-exp-log`

Counts

4 → 108

Calls

4 calls:

1.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
6.0ms	(exp (* (/ b a) (/ b a)))
17.0ms	(* (/ b a) (/ b a))
4.0ms	(log (exp (* (/ b a) (/ b a))))

series127.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(sqrt (fabs (- 1 (log (exp (* (/ b a) (/ b a)))))))
32.0ms	(exp (* (/ b a) (/ b a)))
34.0ms	(* (/ b a) (/ b a))
40.0ms	(log (exp (* (/ b a) (/ b a))))

simplify1.2s

Counts

120 → 120

Iterations

Iter	Nodes
done	2019
3	2019
2	1344
1	433
0	153

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 4.4b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ b a) b)
4.6b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
7.0b	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
46.5b	(posit16->real (real->posit16 (* (/ b a) b)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
19×	`times-frac`
13×	`associate-l`
11×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
4×	`insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-r` `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-l/` `-commutative` `remove-posit16`

Counts

4 → 84

Calls

4 calls:

10.0ms	(* (/ b a) b)
1.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
4.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
0.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

series123.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (/ b a) b)
17.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* (/ b a) b))) a))))
29.0ms	(/ (posit16->real (real->posit16 (* (/ b a) b))) a)
36.0ms	(posit16->real (real->posit16 (* (/ b a) b)))

simplify1.1s

Counts

96 → 96

Iterations

Iter	Nodes
done	2002
3	2002
2	768
1	265
0	129

prune2.2s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.4b

regimes136.0ms

Accuracy

0% (0.1b remaining)

Error of 7.6b against oracle of 7.5b and baseline of 7.6b

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample1.4s

Algorithm

intervals

Results

907.0ms	8000×	body	80	valid
363.0ms	8000×	pre	80	true