Details

sample172.0ms

Algorithm

intervals

Results

87.0ms	135×	body	1280	valid
38.0ms	24×	body	2560	valid
25.0ms	63×	body	640	valid
6.0ms	20×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	4×	body	80	valid

simplify10.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.3b

localize32.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
2.9b	(cos (+ x eps))

rewrite49.0ms

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:

31.0ms	(- (cos (+ x eps)) (cos x))
17.0ms	(cos (+ x eps))

series97.0ms

Counts

2 → 6

Calls

2 calls:

77.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

simplify2.8s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3416
3	1158
2	424
1	202
0	93

prune201.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
2.7b	(sin (/ (fma 2 x eps) 2))

rewrite121.0ms

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:

69.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
43.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
8.0ms	(sin (/ (fma 2 x eps) 2))

series230.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
96.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
44.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.8s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2020
2	602
1	226
0	102

prune418.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (sin (/ (fma 2 x eps) 2)))
2.7b	(sin (/ (fma 2 x eps) 2))
2.7b	(sin (/ (fma 2 x eps) 2))
2.7b	(sin (/ (fma 2 x eps) 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
4.0ms	(sin (/ (fma 2 x eps) 2))
4.0ms	(sin (/ (fma 2 x eps) 2))
6.0ms	(sin (/ (fma 2 x eps) 2))

series277.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(cbrt (sin (/ (fma 2 x eps) 2)))
50.0ms	(sin (/ (fma 2 x eps) 2))
43.0ms	(sin (/ (fma 2 x eps) 2))
50.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.7s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
4	2611
3	800
2	262
1	117
0	60

prune508.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.4b

localize49.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
2.7b	(sin (/ (fma 2 x eps) 2))
2.7b	(sin (/ (fma 2 x eps) 2))
2.7b	(sin (/ (fma 2 x eps) 2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

5×	`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×	`cbrt-prod`
1×	`pow1/3`

Counts

4 → 44

Calls

4 calls:

2.0ms	(cbrt (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
7.0ms	(sin (/ (fma 2 x eps) 2))
4.0ms	(sin (/ (fma 2 x eps) 2))
9.0ms	(sin (/ (fma 2 x eps) 2))

series314.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (log1p (expm1 (sin (/ (fma 2 x eps) 2)))))
54.0ms	(sin (/ (fma 2 x eps) 2))
57.0ms	(sin (/ (fma 2 x eps) 2))
52.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.6s

Counts

56 → 56

Iterations

Iter	Nodes
done	5000
4	2621
3	796
2	271
1	125
0	64

prune482.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.4b

regimes221.0ms

Accuracy

96.3% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.0b

bsearch126.0ms

Steps

Iters	Range		Point
8	9.451876058065096e-06	0.024060934617792813	2.0821597107803942e-05
6	-26711381.42537418	-3720466.2051109266	-3766637.3963067145

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.2s	4388×	body	1280	valid
999.0ms	649×	body	2560	valid
952.0ms	1901×	body	640	valid
193.0ms	689×	body	320	valid
52.0ms	290×	body	160	valid
7.0ms	83×	body	80	valid