Details

sample128.0ms

Algorithm

intervals

Results

48.0ms	106×	body	1280	valid
25.0ms	81×	body	640	valid
10.0ms	372×	pre	80	true
10.0ms	44×	body	320	valid
7.0ms	124×	body	80	valid
2.0ms	17×	body	160	valid

simplify25.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	7
2	7
1	6
0	4

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.6b

localize48.0ms

Local error

Found 1 expressions with local error:

5.8b	(- (exp x) 1.0)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`expm1-log1p-u` `pow1` `sub-neg` `flip3--` `add-cbrt-cube` `diff-log` `add-exp-log` `insert-posit16` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

33.0ms

(- (exp x) 1.0)

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

(- (exp x) 1.0)

simplify4.9s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
4	2165
3	867
2	302
1	149
0	67

prune244.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize47.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (fma 1/6 x 1/2) (* x x) x)
0.0b	(fma 1/6 x 1/2)

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

2×	`add-sqr-sqrt` `expm1-log1p-u` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

2 → 22

Calls

2 calls:

1.0ms	(fma (fma 1/6 x 1/2) (* x x) x)
1.0ms	(fma 1/6 x 1/2)

series102.0ms

Counts

2 → 6

Calls

2 calls:

45.0ms	(fma (fma 1/6 x 1/2) (* x x) x)
56.0ms	(fma 1/6 x 1/2)

simplify7.2s

Counts

28 → 28

Iterations

Iter	Nodes
done	5000
4	3322
3	643
2	171
1	66
0	37

prune317.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize136.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (fma 1/6 x 1/2) (* x x) x)) (cbrt (fma (fma 1/6 x 1/2) (* x x) x)))
0.6b	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
0.6b	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
0.6b	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

23.0ms	(* (cbrt (fma (fma 1/6 x 1/2) (* x x) x)) (cbrt (fma (fma 1/6 x 1/2) (* x x) x)))
5.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
2.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
3.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))

series448.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (cbrt (fma (fma 1/6 x 1/2) (* x x) x)) (cbrt (fma (fma 1/6 x 1/2) (* x x) x)))
104.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
97.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
137.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))

simplify4.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5008
3	1968
2	667
1	283
0	128

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize191.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
0.6b	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
0.6b	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
18.4b	(log (exp (cbrt (fma (fma 1/6 x 1/2) (* x x) x))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

5.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
5.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
5.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
20.0ms	(log (exp (cbrt (fma (fma 1/6 x 1/2) (* x x) x))))

series465.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
108.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
108.0ms	(cbrt (fma (fma 1/6 x 1/2) (* x x) x))
126.0ms	(log (exp (cbrt (fma (fma 1/6 x 1/2) (* x x) x))))

simplify3.7s

Counts

75 → 75

Iterations

Iter	Nodes
done	5000
4	1800
3	664
2	287
1	158
0	92

prune855.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes286.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	6
0	6

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.7s	3456×	body	1280	valid
645.0ms	2480×	body	640	valid
358.0ms	11898×	pre	80	true
251.0ms	1237×	body	320	valid
206.0ms	4073×	body	80	valid
70.0ms	652×	body	160	valid