Details

sample31.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify7.6s

Counts

1 → 1

Iterations

Iter	Nodes
8	6442
7	1455
6	631
5	341
4	166
3	86
2	44
1	19
0	8

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 7.8b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(- 1 (* (/ b a) (/ b a)))
0.4b	(* (/ b a) (/ b a))
7.9b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
40×	`times-frac`
35×	`*-un-lft-identity`
34×	`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×	`expm1-log1p-u` `fma-neg` `prod-diff` `sqrt-prod` `insert-posit16` `log1p-expm1-u`
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 → 109

Calls

3 calls:

5.0ms	(- 1 (* (/ b a) (/ b a)))
26.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series86.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(- 1 (* (/ b a) (/ b a)))
28.0ms	(* (/ b a) (/ b a))
14.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.3s

Counts

118 → 118

Iterations

Iter	Nodes
3	5219
2	1454
1	482
0	167

prune861.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 7.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1 (/ (* b (/ b a)) a))
0.1b	(* b (/ b a))
7.3b	(/ (* b (/ b a)) a)
7.9b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
29×	`add-cube-cbrt`
22×	`times-frac`
21×	`prod-diff`
18×	`add-cbrt-cube` `add-exp-log`
13×	`associate-r`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `fma-neg` `associate-l*` `sqrt-prod`
2×	`associate-*r/` `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 → 120

Calls

4 calls:

8.0ms	(- 1 (/ (* b (/ b a)) a))
9.0ms	(* b (/ b a))
24.0ms	(/ (* b (/ b a)) a)
2.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(- 1 (/ (* b (/ b a)) a))
35.0ms	(* b (/ b a))
50.0ms	(/ (* b (/ b a)) a)
13.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify8.2s

Counts

132 → 132

Iterations

Iter	Nodes
3	8843
2	1575
1	484
0	199

prune790.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 7.7b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* b (/ b a))
7.3b	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
7.9b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
45.8b	(posit16->real (real->posit16 (* b (/ b a))))

rewrite40.0ms

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:

26.0ms	(* b (/ b a))
8.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
2.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
1.0ms	(posit16->real (real->posit16 (* b (/ b a))))

series124.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* b (/ b a))
44.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
16.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
21.0ms	(posit16->real (real->posit16 (* b (/ b a))))

simplify1.9s

Counts

104 → 104

Iterations

Iter	Nodes
3	3843
2	871
1	277
0	136

prune1.8s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 7.7b

localize63.0ms

Local error

Found 4 expressions with local error:

7.9b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
45.8b	(posit16->real (real->posit16 (* b (/ b a))))
45.8b	(posit16->real (real->posit16 (* b (/ b a))))
45.8b	(posit16->real (real->posit16 (* b (/ b a))))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`sqrt-prod` `remove-posit16`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 49

Calls

4 calls:

2.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
0.0ms	(posit16->real (real->posit16 (* b (/ b a))))
0.0ms	(posit16->real (real->posit16 (* b (/ b a))))
0.0ms	(posit16->real (real->posit16 (* b (/ b a))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
20.0ms	(posit16->real (real->posit16 (* b (/ b a))))
33.0ms	(posit16->real (real->posit16 (* b (/ b a))))
29.0ms	(posit16->real (real->posit16 (* b (/ b a))))

simplify6.9s

Counts

61 → 61

Iterations

Iter	Nodes
5	6171
4	1371
3	416
2	135
1	63
0	45

prune1.3s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 7.7b

regimes137.0ms

Accuracy

0% (0.1b remaining)

Error of 7.7b against oracle of 7.6b and baseline of 7.7b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
1	8
0	8

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.2s	8000×	body	80	valid
334.0ms	8000×	pre	80	true