Details

sample159.0ms

Algorithm

intervals

Results

76.0ms	106×	body	1280	valid
27.0ms	19×	body	2560	valid
27.0ms	57×	body	640	valid
10.0ms	30×	body	320	valid
4.0ms	36×	body	80	valid
2.0ms	8×	body	160	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune40.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.7b

localize15.0ms

Local error

Found 2 expressions with local error:

1.1b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite90.0ms

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:

78.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series71.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (sin (+ x eps)) (sin x))
22.0ms	(sin (+ x eps))

simplify2.7s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3934
3	1269
2	446
1	203
0	92

prune254.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.4b

localize41.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

14.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series127.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
42.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.1s

Counts

38 → 38

Iterations

Iter	Nodes
done	5001
4	2632
3	983
2	353
1	150
0	70

prune248.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.3b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
0.3b	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.4b	(expm1 (cos (/ (fma 2 x eps) 2)))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite23.0ms

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:

0.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
18.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
0.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series301.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(log1p (expm1 (cos (/ (fma 2 x eps) 2))))
107.0ms	(* (sin (/ eps 2)) (log1p (expm1 (cos (/ (fma 2 x eps) 2)))))
86.0ms	(expm1 (cos (/ (fma 2 x eps) 2)))
34.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.7s

Counts

67 → 67

Iterations

Iter	Nodes
done	5002
4	3729
3	1303
2	469
1	206
0	97

prune277.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (log1p (expm1 (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))))
0.3b	(log1p (cos (/ (fma 2 x eps) 2)))
0.4b	(expm1 (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
2.9b	(cos (/ (fma 2 x eps) 2))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

13.0ms	(* (sin (/ eps 2)) (log1p (expm1 (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))))
0.0ms	(log1p (cos (/ (fma 2 x eps) 2)))
0.0ms	(expm1 (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
4.0ms	(cos (/ (fma 2 x eps) 2))

series294.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(* (sin (/ eps 2)) (log1p (expm1 (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))))
53.0ms	(log1p (cos (/ (fma 2 x eps) 2)))
89.0ms	(expm1 (expm1 (log1p (cos (/ (fma 2 x eps) 2)))))
32.0ms	(cos (/ (fma 2 x eps) 2))

simplify3.1s

Counts

67 → 67

Iterations

Iter	Nodes
done	5000
4	4258
3	1413
2	525
1	230
0	112

prune355.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.3b

regimes146.0ms

Accuracy

96.8% (0.4b remaining)

Error of 0.8b against oracle of 0.4b and baseline of 14.5b

bsearch136.0ms

Steps

Iters	Range		Point
7	8.635844677648429e-30	2.196855215494652e-27	2.1464224965526296e-27
10	-1.4244285555183042e-05	-9.550132857780223e-23	-7.141151458641036e-09

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	26

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.6s	3276×	body	1280	valid
1.2s	1801×	body	640	valid
893.0ms	658×	body	2560	valid
731.0ms	769×	body	320	valid
142.0ms	352×	body	160	valid
133.0ms	1144×	body	80	valid