Details

sample187.0ms

Algorithm

intervals

Results

88.0ms	145×	body	1280	valid
29.0ms	19×	body	2560	valid
26.0ms	13×	body	160	valid
25.0ms	53×	body	640	valid
9.0ms	24×	body	320	valid
0.0ms	2×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize13.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (cos (+ x eps)) (cos x))
2.8b	(cos (+ x eps))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

12.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series114.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (cos (+ x eps)) (cos x))
49.0ms	(cos (+ x eps))

simplify1.2s

Counts

48 → 48

Iterations

Iter	Nodes
done	2010
4	2010
3	1158
2	424
1	202
0	93

prune212.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 54

Calls

3 calls:

26.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
13.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series193.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
74.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
32.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.3s

Counts

63 → 63

Iterations

Iter	Nodes
done	2003
4	2003
3	1742
2	577
1	226
0	102

prune375.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

27.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series126.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
42.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.4s

Counts

37 → 37

Iterations

Iter	Nodes
done	2003
4	2003
3	1661
2	459
1	173
0	73

prune204.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
0.3b	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
0.4b	(log1p (sin (/ (fma 2 x eps) 2)))
3.0b	(sin (/ (fma 2 x eps) 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

0.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
18.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
5.0ms	(sin (/ (fma 2 x eps) 2))

series312.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(expm1 (log1p (sin (/ (fma 2 x eps) 2))))
131.0ms	(* (* -2 (sin (/ eps 2))) (expm1 (log1p (sin (/ (fma 2 x eps) 2)))))
61.0ms	(log1p (sin (/ (fma 2 x eps) 2)))
40.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.3s

Counts

67 → 67

Iterations

Iter	Nodes
done	2001
4	2001
3	1794
2	575
1	217
0	99

prune367.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes198.0ms

Accuracy

97.6% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.7b

bsearch281.0ms

Steps

Iters	Range		Point
10	3.4946005567744297e-15	3231.8276777318033	8.193560063624595e-05
10	-190824653340.76273	-0.005838610583870787	-0.005924238612320757

simplify10.0ms

Iterations

Iter	Nodes
done	33
1	33
0	29

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.1s	4480×	body	1280	valid
1.3s	1864×	body	640	valid
1.1s	641×	body	2560	valid
608.0ms	640×	body	320	valid
77.0ms	305×	body	160	valid
9.0ms	70×	body	80	valid