Details

sample112.0ms

Algorithm

intervals

Results

70.0ms	85×	body	10240	exit
22.0ms	270×	body	80	valid
3.0ms	5×	body	640	valid
2.0ms	8×	body	160	valid
1.0ms	1×	body	1280	valid
1.0ms	3×	body	320	valid

simplify12.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	26
3	26
2	22
1	15
0	8

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (log1p (exp x)) (* y x))
0.7b	(log1p (exp x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-log-exp`
4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-neg` `prod-diff`
2×	`pow1` `log1p-udef` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `log1p-expm1` `flip--`

Counts

2 → 34

Calls

2 calls:

7.0ms	(- (log1p (exp x)) (* y x))
1.0ms	(log1p (exp x))

series132.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(- (log1p (exp x)) (* y x))
73.0ms	(log1p (exp x))

simplify801.0ms

Counts

40 → 40

Iterations

Iter	Nodes
done	2002
3	1021
2	320
1	128
0	61

prune127.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (- (log1p (exp x)) (* y x)))
0.0b	(- (log1p (exp x)) (* y x))
0.7b	(log1p (exp x))
1.1b	(expm1 (log1p (- (log1p (exp x)) (* y x))))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
6×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt`
4×	`pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`log1p-udef` `fma-neg` `prod-diff`
2×	`diff-log` `log1p-expm1`
1×	`expm1-log1p` `sub-neg` `flip3--` `flip--` `expm1-udef`

Counts

4 → 58

Calls

4 calls:

1.0ms	(log1p (- (log1p (exp x)) (* y x)))
7.0ms	(- (log1p (exp x)) (* y x))
0.0ms	(log1p (exp x))
0.0ms	(expm1 (log1p (- (log1p (exp x)) (* y x))))

series616.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(log1p (- (log1p (exp x)) (* y x)))
55.0ms	(- (log1p (exp x)) (* y x))
58.0ms	(log1p (exp x))
285.0ms	(expm1 (log1p (- (log1p (exp x)) (* y x))))

simplify665.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	2002
2	1225
1	386
0	152

prune344.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma x (fma x 1/8 1/2) (log 2))
0.0b	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`fma-neg` `prod-diff`
2×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate--l+` `flip--`

Counts

2 → 33

Calls

2 calls:

0.0ms	(fma x (fma x 1/8 1/2) (log 2))
5.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

series91.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(fma x (fma x 1/8 1/2) (log 2))
51.0ms	(- (fma x (fma x 1/8 1/2) (log 2)) (* y x))

simplify750.0ms

Counts

39 → 39

Iterations

Iter	Nodes
done	2000
3	1794
2	357
1	131
0	59

prune191.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x (fma x 1/8 1/2) (log 2))
0.0b	(- (posit16->real (real->posit16 (fma x (fma x 1/8 1/2) (log 2)))) (* y x))
37.4b	(posit16->real (real->posit16 (fma x (fma x 1/8 1/2) (log 2))))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `fma-neg` `prod-diff` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `fma-udef` `remove-posit16` `flip--`

Counts

3 → 43

Calls

3 calls:

0.0ms	(fma x (fma x 1/8 1/2) (log 2))
5.0ms	(- (posit16->real (real->posit16 (fma x (fma x 1/8 1/2) (log 2)))) (* y x))
0.0ms	(posit16->real (real->posit16 (fma x (fma x 1/8 1/2) (log 2))))

series122.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(fma x (fma x 1/8 1/2) (log 2))
51.0ms	(- (posit16->real (real->posit16 (fma x (fma x 1/8 1/2) (log 2)))) (* y x))
42.0ms	(posit16->real (real->posit16 (fma x (fma x 1/8 1/2) (log 2))))

simplify1.0s

Counts

52 → 52

Iterations

Iter	Nodes
done	2000
3	1936
2	408
1	143
0	69

prune457.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes115.0ms

Accuracy

0% (0.3b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	7
1	7
0	6

end0.0ms

sample3.6s

Algorithm

intervals

Results

2.3s	2380×	body	10240	exit
759.0ms	8332×	body	80	valid
119.0ms	263×	body	640	valid
90.0ms	119×	body	1280	valid
61.0ms	210×	body	320	valid
21.0ms	122×	body	160	valid