Details

sample41.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5216
6	2493
5	808
4	236
3	88
2	44
1	19
0	8

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.5b

localize28.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
4.5b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite56.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 86

Calls

2 calls:

48.0ms	(* (/ b a) (/ b a))
3.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series71.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(* (/ b a) (/ b a))
25.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.7s

Counts

92 → 92

Iterations

Iter	Nodes
done	5001
3	4044
2	1310
1	407
0	134

prune442.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 4.5b

localize31.0ms

Local error

Found 3 expressions with local error:

0.2b	(* b (/ b a))
4.5b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
7.2b	(/ (* b (/ b a)) a)

rewrite50.0ms

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-r`
6×	`pow1`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `associate-/r` `associate-l*` `sqrt-prod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`associate-*r/` `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 → 78

Calls

3 calls:

21.0ms	(* b (/ b a))
2.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
25.0ms	(/ (* b (/ b a)) a)

series76.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(* b (/ b a))
21.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))
33.0ms	(/ (* b (/ b a)) a)

simplify1.2s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1053
1	293
0	122

prune436.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
0.4b	(* (/ b a) (/ b a))
2.2b	(expm1 (log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
4.5b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
33×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `add-exp-log`
13×	`swap-sqr` `associate-r` `associate-l`
12×	`pow1`
5×	`expm1-log1p-u`
4×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
1×	`pow2` `frac-times` `rem-sqrt-square` `log1p-udef` `expm1-log1p` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `associate-l/` `log1p-expm1` `associate-r/` `pow-sqr` `*-commutative` `pow-prod-up` `expm1-udef`

Counts

4 → 110

Calls

4 calls:

0.0ms	(log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
30.0ms	(* (/ b a) (/ b a))
0.0ms	(expm1 (log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series235.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a))))))
54.0ms	(* (/ b a) (/ b a))
96.0ms	(expm1 (log1p (sqrt (fabs (- 1 (* (/ b a) (/ b a)))))))
18.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.9s

Counts

122 → 122

Iterations

Iter	Nodes
done	5567
3	4053
2	1432
1	450
0	159

prune617.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 4.5b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (/ b a))
4.5b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
7.2b	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
46.3b	(posit16->real (real->posit16 (* b (/ b a))))

rewrite39.0ms

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×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `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 → 92

Calls

4 calls:

29.0ms	(* b (/ b a))
1.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
5.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
0.0ms	(posit16->real (real->posit16 (* b (/ b a))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* b (/ b a))
25.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
38.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
24.0ms	(posit16->real (real->posit16 (* b (/ b a))))

simplify2.6s

Counts

104 → 104

Iterations

Iter	Nodes
done	5008
3	3704
2	841
1	281
0	136

prune945.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.5b

regimes187.0ms

Accuracy

0% (0.1b remaining)

Error of 7.1b against oracle of 7.1b and baseline of 7.1b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	10
1	10
0	8

end0.0ms

sample974.0ms

Algorithm

intervals

Results

504.0ms	8000×	body	80	valid
322.0ms	8000×	pre	80	true