Details

sample229.0ms

Algorithm

intervals

Results

118.0ms	143×	body	1280	valid
53.0ms	30×	body	2560	valid
39.0ms	55×	body	640	valid
6.0ms	16×	body	320	valid
2.0ms	9×	body	160	valid
0.0ms	3×	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: 41.6b

localize39.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (cos (+ x eps)) (cos x))
3.5b	(cos (+ x eps))

rewrite23.0ms

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))
10.0ms	(cos (+ x eps))

series137.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (cos (+ x eps)) (cos x))
38.0ms	(cos (+ x eps))

simplify1.5s

Counts

48 → 48

Iterations

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

prune216.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize25.0ms

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)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite70.0ms

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:

39.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
24.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
5.0ms	(sin (/ (fma 2 x eps) 2))

series241.0ms

Counts

3 → 9

Calls

3 calls:

115.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
73.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
53.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.6s

Counts

63 → 63

Iterations

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

prune443.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.3b

localize41.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))) -2)
0.3b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`associate-l` `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-*l/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

44.0ms	(* (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))) -2)
24.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series218.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(* (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))) -2)
73.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
54.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.5s

Counts

63 → 63

Iterations

Iter	Nodes
done	2008
4	2008
3	1696
2	587
1	235
0	104

prune423.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.3b

localize63.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma 2 x eps) 2)))
0.3b	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 55

Calls

4 calls:

1.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
0.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
19.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
7.0ms	(sin (/ (fma 2 x eps) 2))

series402.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(expm1 (sin (/ (fma 2 x eps) 2)))
107.0ms	(log1p (expm1 (sin (/ (fma 2 x eps) 2))))
153.0ms	(* (sin (/ eps 2)) (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
52.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.8s

Counts

67 → 67

Iterations

Iter	Nodes
done	2014
5	2014
4	1974
3	911
2	408
1	185
0	93

prune385.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

regimes275.0ms

Accuracy

97.5% (0.4b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.5b

bsearch285.0ms

Steps

Iters	Range		Point
11	0.1386194397507998	2.0351360940656854e+23	0.14106810261025804
10	-114.47745452469812	-1.7358418861219995e-09	-0.000549063754430864

simplify9.0ms

Iterations

Iter	Nodes
done	31
1	31
0	27

end0.0ms

sample9.1s

Algorithm

intervals

Results

5.8s	4433×	body	1280	valid
1.3s	1883×	body	640	valid
1.2s	607×	body	2560	valid
400.0ms	715×	body	320	valid
85.0ms	293×	body	160	valid
10.0ms	69×	body	80	valid