Details

sample33.0ms

Algorithm

intervals

Results

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

simplify7.8s

Counts

1 → 1

Iterations

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.9b

localize31.0ms

Local error

Found 2 expressions with local error:

0.4b	(* (/ b a) (/ b a))
10.0b	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

rewrite19.0ms

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:

15.0ms	(* (/ b a) (/ b a))
2.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

series49.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* (/ b a) (/ b a))
14.0ms	(sqrt (fabs (- 1 (* (/ b a) (/ b a)))))

simplify2.3s

Counts

92 → 92

Iterations

Iter	Nodes
3	4437
2	1250
1	398
0	134

prune920.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 9.9b

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(* b (/ b a))
6.7b	(/ (* b (/ b a)) a)
10.0b	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

rewrite451.0ms

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:

424.0ms	(* b (/ b a))
23.0ms	(/ (* b (/ b a)) a)
3.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

series86.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(* b (/ b a))
32.0ms	(/ (* b (/ b a)) a)
22.0ms	(sqrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify3.2s

Counts

87 → 87

Iterations

Iter	Nodes
3	5336
2	953
1	283
0	122

prune904.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 9.8b

localize52.0ms

Local error

Found 4 expressions with local error:

6.7b	(/ (* b (/ b a)) a)
10.3b	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))
10.3b	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))
10.3b	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-cbrt-cube` `add-exp-log`
9×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*` `times-frac` `pow1/3`
2×	`prod-exp` `cbrt-unprod`
1×	`clear-num` `frac-2neg` `associate-r/` `div-inv` `associate-/l` `associate-/l/`

Counts

4 → 69

Calls

4 calls:

16.0ms	(/ (* b (/ b a)) a)
1.0ms	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))
1.0ms	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))
1.0ms	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))

series264.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (* b (/ b a)) a)
70.0ms	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))
68.0ms	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))
81.0ms	(cbrt (fabs (- 1 (/ (* b (/ b a)) a))))

simplify2.4s

Counts

81 → 81

Iterations

Iter	Nodes
3	4626
2	724
1	195
0	82

prune1.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 9.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* b (/ b a))
6.7b	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
10.0b	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
47.3b	(posit16->real (real->posit16 (* b (/ b a))))

rewrite31.0ms

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:

18.0ms	(* 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))))

series123.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* b (/ b a))
39.0ms	(/ (posit16->real (real->posit16 (* b (/ b a)))) a)
13.0ms	(sqrt (fabs (- 1 (/ (posit16->real (real->posit16 (* b (/ b a)))) a))))
38.0ms	(posit16->real (real->posit16 (* b (/ b a))))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
3	3843
2	871
1	277
0	136

prune1.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 9.8b

regimes162.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
1	8
0	8

end0.0ms

sample1.5s

Algorithm

intervals

Results

928.0ms	8000×	body	80	valid
353.0ms	8000×	pre	80	true