Details

sample192.0ms

Algorithm

intervals

Results

94.0ms	106×	body	1280	valid
43.0ms	30×	body	2560	valid
27.0ms	49×	body	640	valid
9.0ms	26×	body	320	valid
4.0ms	34×	body	80	valid
3.0ms	11×	body	160	valid

simplify5.0ms

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: 39.5b

localize50.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite59.0ms

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` `add-cbrt-cube` `sin-sum` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

51.0ms	(- (sin (+ x eps)) (sin x))
7.0ms	(sin (+ x eps))

series68.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(- (sin (+ x eps)) (sin x))
26.0ms	(sin (+ x eps))

simplify1.3s

Counts

48 → 48

Iterations

Iter	Nodes
done	2012
4	2012
3	1269
2	446
1	203
0	92

prune155.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
0.2b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.7b	(cos (/ (fma 2 x eps) 2))

rewrite54.0ms

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-cos-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

30.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
18.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
5.0ms	(cos (/ (fma 2 x eps) 2))

series171.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
59.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
37.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.1s

Counts

63 → 63

Iterations

Iter	Nodes
done	2000
3	2000
2	629
1	235
0	100

prune423.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize39.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* 2 (sin (/ eps 2))) (cos (/ (fma 2 x eps) 2)))
3.7b	(cos (/ (fma 2 x eps) 2))

rewrite43.0ms

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:

38.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (fma 2 x eps) 2)))
5.0ms	(cos (/ (fma 2 x eps) 2))

series133.0ms

Counts

2 → 6

Calls

2 calls:

87.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (fma 2 x eps) 2)))
46.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.5s

Counts

37 → 37

Iterations

Iter	Nodes
done	2012
4	2012
3	1924
2	514
1	179
0	72

prune255.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 2 (sin (/ eps 2))) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.3b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
3.7b	(cos (/ (fma 2 x eps) 2))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `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:

39.0ms	(* (* 2 (sin (/ eps 2))) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
3.0ms	(cos (/ (fma 2 x eps) 2))

series665.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (* 2 (sin (/ eps 2))) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
84.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
411.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
31.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.3s

Counts

67 → 67

Iterations

Iter	Nodes
done	2002
3	2002
2	641
1	243
0	104

prune465.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.4b

regimes230.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 15.5b

bsearch319.0ms

Steps

Iters	Range		Point
11	7.248271131626031e-34	1.9659298028413272e-13	1.9470983410706072e-13
10	-114.47745452469812	-1.7358418861219995e-09	-7.3997675699750705e-09

simplify9.0ms

Iterations

Iter	Nodes
done	32
1	32
0	24

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.6s	3311×	body	1280	valid
1.7s	1852×	body	640	valid
1.1s	607×	body	2560	valid
326.0ms	772×	body	320	valid
196.0ms	1114×	body	80	valid
91.0ms	344×	body	160	valid