Details

sample276.0ms

Algorithm

intervals

Results

103.0ms	56×	body	10240	exit
61.0ms	64×	body	1280	valid
41.0ms	316×	body	80	valid
32.0ms	48×	body	640	valid
7.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
4	1436
3	398
2	124
1	49
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ -1 eps))
0.0b	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps))))
0.0b	(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
3.9b	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

406×	`add-sqr-sqrt`
327×	`times-frac`
301×	`*-un-lft-identity`
180×	`prod-diff`
144×	`add-cube-cbrt`
104×	`difference-of-squares`
59×	`fma-udef`
57×	`exp-sum`
51×	`difference-of-sqr-1`
35×	`distribute-lft-out--`
21×	`div-inv`
14×	`associate-/l*`
8×	`add-cbrt-cube`
7×	`add-exp-log`
6×	`pow1` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r` `associate-r*` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `associate-l`
2×	`flip3--` `div-sub` `associate-*r/` `flip--` `associate-/l/`
1×	`distribute-rgt-in` `cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `associate--l+` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out` `associate--r-` `unswap-sqr`

Counts

4 → 332

Calls

4 calls:

26.0ms	(* x (+ -1 eps))
0.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps))))
54.0ms	(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
28.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

series270.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* x (+ -1 eps))
34.0ms	(fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps))))
44.0ms	(/ (- (/ 1 eps) 1) (exp (fma eps x x)))
149.0ms	(- (fma (exp (* x (+ -1 eps))) (/ 1 eps) (exp (* x (+ -1 eps)))) (/ (- (/ 1 eps) 1) (exp (fma eps x x))))

simplify2.2s

Counts

344 → 344

Iterations

Iter	Nodes
done	5001
2	3825
1	1412
0	537

prune2.2s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.4b

localize16.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (* x x) x)
5.6b	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1`
7×	`add-cbrt-cube` `add-exp-log`
6×	`pow-plus` `pow-prod-up`
4×	`add-sqr-sqrt`
3×	`-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`pow2` `expm1-log1p-u` `pow-sqr` `insert-posit16` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `pow3` `*-commutative` `fma-udef` `unswap-sqr`

Counts

2 → 42

Calls

2 calls:

24.0ms	(* (* x x) x)
1.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

series94.0ms

Counts

2 → 6

Calls

2 calls:

59.0ms	(* (* x x) x)
35.0ms	(fma (* (* x x) x) 2/3 (- 2 (* x x)))

simplify1.9s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	1580
3	616
2	267
1	122
0	55

prune183.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize26.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (* x x) (fma x 2/3 -1) 2)
0.1b	(fma x 2/3 -1)

rewrite1.0ms

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:

0.0ms	(fma (* x x) (fma x 2/3 -1) 2)
0.0ms	(fma x 2/3 -1)

series81.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(fma (* x x) (fma x 2/3 -1) 2)
41.0ms	(fma x 2/3 -1)

simplify2.3s

Counts

28 → 28

Iterations

Iter	Nodes
done	5002
4	1425
3	411
2	148
1	66
0	38

prune136.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (* x x) (posit16->real (real->posit16 (fma x 2/3 -1))) 2)
0.1b	(fma x 2/3 -1)
13.0b	(posit16->real (real->posit16 (fma x 2/3 -1)))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 33

Calls

3 calls:

0.0ms	(fma (* x x) (posit16->real (real->posit16 (fma x 2/3 -1))) 2)
0.0ms	(fma x 2/3 -1)
0.0ms	(posit16->real (real->posit16 (fma x 2/3 -1)))

series160.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(fma (* x x) (posit16->real (real->posit16 (fma x 2/3 -1))) 2)
62.0ms	(fma x 2/3 -1)
53.0ms	(posit16->real (real->posit16 (fma x 2/3 -1)))

simplify2.0s

Counts

42 → 42

Iterations

Iter	Nodes
done	5009
4	1702
3	507
2	189
1	80
0	49

prune354.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes111.0ms

Accuracy

95.9% (0.7b remaining)

Error of 1.1b against oracle of 0.4b and baseline of 16.5b

bsearch180.0ms

Steps

Iters	Range		Point
8	5.220773054910798	2842.495256040047	64.8190525609748

simplify390.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample8.9s

Algorithm

intervals

Results

3.1s	1901×	body	10240	exit
2.1s	1680×	body	1280	valid
1.5s	10104×	body	80	valid
1.3s	1287×	body	640	valid
330.0ms	644×	body	320	valid
77.0ms	320×	body	160	valid