Details

sample377.0ms

Algorithm

intervals

Results

118.0ms	58×	body	10240	exit
81.0ms	58×	body	1280	valid
65.0ms	306×	body	80	valid
64.0ms	42×	body	640	valid
13.0ms	24×	body	320	valid
7.0ms	13×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Iter	Nodes
5	3307
4	836
3	312
2	122
1	47
0	19

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 32.1b

localize64.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma eps (- x) (- x)))
0.0b	(exp (fma x eps (- x)))
0.0b	(exp (fma x eps (- x)))
4.9b	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x)))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`exp-prod`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `fma-udef` `insert-posit16` `log1p-expm1-u`
3×	`exp-sum` `rem-exp-log`

Counts

4 → 56

Calls

4 calls:

4.0ms	(exp (fma eps (- x) (- x)))
4.0ms	(exp (fma x eps (- x)))
4.0ms	(exp (fma x eps (- x)))
1.0ms	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x)))))

series229.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(exp (fma eps (- x) (- x)))
19.0ms	(exp (fma x eps (- x)))
16.0ms	(exp (fma x eps (- x)))
158.0ms	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (exp (fma x eps (- x)))))

simplify3.4s

Counts

68 → 68

Iterations

Iter	Nodes
4	3983
3	1107
2	411
1	173
0	89

prune947.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 2 expressions with local error:

0.3b	(* x 2/3)
5.8b	(fma (* x 2/3) (* x x) (- 2 (* x x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

11.0ms	(* x 2/3)
1.0ms	(fma (* x 2/3) (* x x) (- 2 (* x x)))

series78.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(* x 2/3)
53.0ms	(fma (* x 2/3) (* x x) (- 2 (* x x)))

simplify1.4s

Counts

38 → 38

Iterations

Iter	Nodes
4	3494
3	736
2	218
1	100
0	54

prune344.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(* x 2/3)
0.4b	(expm1 (log1p (fma (* x 2/3) (* x x) (- 2 (* x x)))))
5.8b	(fma (* x 2/3) (* x x) (- 2 (* x x)))
11.0b	(log1p (fma (* x 2/3) (* x x) (- 2 (* x x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
5×	`expm1-log1p-u`
4×	`insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l`
1×	`log1p-udef` `expm1-log1p` `pow-prod-down` `prod-exp` `log1p-expm1` `*-commutative` `cbrt-unprod` `fma-udef` `expm1-udef` `unswap-sqr`

Counts

4 → 56

Calls

4 calls:

16.0ms	(* x 2/3)
0.0ms	(expm1 (log1p (fma (* x 2/3) (* x x) (- 2 (* x x)))))
0.0ms	(fma (* x 2/3) (* x x) (- 2 (* x x)))
1.0ms	(log1p (fma (* x 2/3) (* x x) (- 2 (* x x))))

series283.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* x 2/3)
120.0ms	(expm1 (log1p (fma (* x 2/3) (* x x) (- 2 (* x x)))))
62.0ms	(fma (* x 2/3) (* x x) (- 2 (* x x)))
82.0ms	(log1p (fma (* x 2/3) (* x x) (- 2 (* x x))))

simplify4.4s

Counts

68 → 68

Iterations

Iter	Nodes
4	7230
3	1841
2	640
1	253
0	120

prune544.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (fma eps (- x) (- x)))
0.0b	(exp (fma x eps (- x)))
0.0b	(pow E (fma x eps (- x)))
4.9b	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (pow E (fma x eps (- x)))))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`exp-prod` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `fma-udef` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `unpow-prod-down`
2×	`exp-sum` `pow-exp` `rem-exp-log`
1×	`pow-to-exp` `unpow-prod-up` `e-exp-1` `pow-pow` `sqr-pow`

Counts

4 → 63

Calls

4 calls:

2.0ms	(exp (fma eps (- x) (- x)))
2.0ms	(exp (fma x eps (- x)))
2.0ms	(pow E (fma x eps (- x)))
0.0ms	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (pow E (fma x eps (- x)))))

series308.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(exp (fma eps (- x) (- x)))
25.0ms	(exp (fma x eps (- x)))
38.0ms	(pow E (fma x eps (- x)))
210.0ms	(fma (/ 1 eps) (exp (fma x eps (- x))) (fma (exp (fma eps (- x) (- x))) (- 1 (/ 1 eps)) (pow E (fma x eps (- x)))))

simplify7.7s

Counts

75 → 75

Iterations

Iter	Nodes
4	6367
3	1671
2	574
1	239
0	118

prune1.2s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes77.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.5b

bsearch246.0ms

Steps

Iters	Range		Point
9	9.810191608759935e-05	3826.660001831638	115.92419819178706

simplify5.0ms

Iterations

Iter	Nodes
2	26
1	26
0	25

end0.0ms

sample11.8s

Algorithm

intervals

Results

3.1s	1912×	body	10240	exit
3.0s	1732×	body	1280	valid
2.3s	10030×	body	80	valid
2.0s	1267×	body	640	valid
991.0ms	685×	body	320	valid
105.0ms	290×	body	160	valid