Details

sample201.0ms

Algorithm

intervals

Results

113.0ms	145×	body	1280	valid
36.0ms	22×	body	2560	valid
27.0ms	55×	body	640	valid
11.0ms	26×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify9.0ms

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: 38.6b

localize25.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.4b	(cos (+ x eps))

rewrite76.0ms

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:

27.0ms	(- (cos (+ x eps)) (cos x))
48.0ms	(cos (+ x eps))

series106.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (cos (+ x eps)) (cos x))
28.0ms	(cos (+ x eps))

simplify975.0ms

Counts

48 → 48

Iterations

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

prune217.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

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)))
2.4b	(sin (/ (fma 2 x eps) 2))

rewrite65.0ms

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:

42.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
19.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series197.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
77.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
42.0ms	(sin (/ (fma 2 x eps) 2))

simplify893.0ms

Counts

63 → 63

Iterations

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

prune379.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
2.4b	(sin (/ (fma 2 x eps) 2))

rewrite44.0ms

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:

40.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series179.0ms

Counts

2 → 6

Calls

2 calls:

124.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
55.0ms	(sin (/ (fma 2 x eps) 2))

simplify915.0ms

Counts

37 → 37

Iterations

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

prune334.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
0.6b	(cbrt (sin (/ eps 2)))
2.4b	(sin (/ (fma 2 x eps) 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

3.0ms	(cbrt (sin (/ eps 2)))
3.0ms	(cbrt (sin (/ eps 2)))
3.0ms	(cbrt (sin (/ eps 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series482.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (sin (/ eps 2)))
113.0ms	(cbrt (sin (/ eps 2)))
166.0ms	(cbrt (sin (/ eps 2)))
64.0ms	(sin (/ (fma 2 x eps) 2))

simplify589.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	2000
3	683
2	234
1	119
0	63

prune391.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.3b

regimes288.0ms

Accuracy

97.4% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 14.6b

bsearch210.0ms

Steps

Iters	Range		Point
10	0.0038666078177206752	941504501108.8118	0.00391800888554098
10	-121993772661.31783	-0.22068356154967622	-0.22306452923435388

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	24

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.6s	4457×	body	1280	valid
1.7s	1832×	body	640	valid
1.2s	665×	body	2560	valid
302.0ms	668×	body	320	valid
122.0ms	298×	body	160	valid
10.0ms	80×	body	80	valid