Details

sample251.0ms

Algorithm

intervals

Results

152.0ms	142×	body	1280	valid
34.0ms	69×	body	640	valid
28.0ms	16×	body	2560	valid
6.0ms	17×	body	320	valid
3.0ms	11×	body	160	valid
0.0ms	1×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.1b

localize25.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `cos-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `flip--` `diff-cos` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

33.0ms	(- (cos (+ x eps)) (cos x))
21.0ms	(cos (+ x eps))

series142.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(- (cos (+ x eps)) (cos x))
50.0ms	(cos (+ x eps))

simplify5.4s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3496
3	1197
2	427
1	201
0	91

prune375.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize49.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
4.6b	(sin (/ (fma 2 x eps) 2))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

87.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
51.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
11.0ms	(sin (/ (fma 2 x eps) 2))

series301.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
110.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
64.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.1s

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
3	1975
2	609
1	230
0	101

prune647.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize51.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (* eps 1/2))) (sin (/ (fma 2 x eps) 2)))
4.6b	(sin (/ (fma 2 x eps) 2))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative`

Counts

2 → 29

Calls

2 calls:

70.0ms	(* (* -2 (sin (* eps 1/2))) (sin (/ (fma 2 x eps) 2)))
8.0ms	(sin (/ (fma 2 x eps) 2))

series174.0ms

Counts

2 → 6

Calls

2 calls:

111.0ms	(* (* -2 (sin (* eps 1/2))) (sin (/ (fma 2 x eps) 2)))
63.0ms	(sin (/ (fma 2 x eps) 2))

simplify4.2s

Counts

35 → 35

Iterations

Iter	Nodes
done	5002
3	1656
2	488
1	175
0	73

prune427.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize75.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (fma eps 1/2 x)))
0.3b	(* (* -2 (sin (* eps 1/2))) (log1p (expm1 (sin (fma eps 1/2 x)))))
0.3b	(log1p (expm1 (sin (fma eps 1/2 x))))
4.6b	(sin (fma eps 1/2 x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

1.0ms	(expm1 (sin (fma eps 1/2 x)))
75.0ms	(* (* -2 (sin (* eps 1/2))) (log1p (expm1 (sin (fma eps 1/2 x)))))
1.0ms	(log1p (expm1 (sin (fma eps 1/2 x))))
6.0ms	(sin (fma eps 1/2 x))

series402.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(expm1 (sin (fma eps 1/2 x)))
176.0ms	(* (* -2 (sin (* eps 1/2))) (log1p (expm1 (sin (fma eps 1/2 x)))))
121.0ms	(log1p (expm1 (sin (fma eps 1/2 x))))
43.0ms	(sin (fma eps 1/2 x))

simplify6.5s

Counts

64 → 64

Iterations

Iter	Nodes
done	5001
4	3917
3	1719
2	563
1	211
0	97

prune538.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes457.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	22
1	22
0	16

end0.0ms

sample9.3s

Algorithm

intervals

Results

5.2s	4443×	body	1280	valid
1.8s	1849×	body	640	valid
1.4s	646×	body	2560	valid
430.0ms	691×	body	320	valid
65.0ms	293×	body	160	valid
9.0ms	78×	body	80	valid