Details

sample263.0ms

Algorithm

intervals

Results

158.0ms	120×	body	1280	valid
39.0ms	59×	body	640	valid
38.0ms	20×	body	2560	valid
6.0ms	13×	body	320	valid
5.0ms	31×	body	80	valid
4.0ms	13×	body	160	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: 36.5b

localize29.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (sin (+ x eps)) (sin x))
2.8b	(sin (+ x eps))

rewrite83.0ms

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:

67.0ms	(- (sin (+ x eps)) (sin x))
14.0ms	(sin (+ x eps))

series82.0ms

Counts

2 → 6

Calls

2 calls:

49.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify1.2s

Counts

48 → 48

Iterations

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

prune219.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize37.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
3.0b	(cos (/ (fma 2 x eps) 2))

rewrite30.0ms

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:

23.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
6.0ms	(cos (/ (fma 2 x eps) 2))

series133.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
51.0ms	(cos (/ (fma 2 x eps) 2))

simplify1.1s

Counts

38 → 38

Iterations

Iter	Nodes
done	2036
4	2036
3	983
2	353
1	150
0	70

prune189.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize25.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cos (fma eps 1/2 x)))
3.0b	(cos (fma eps 1/2 x))

rewrite30.0ms

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×	`cos-sum` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `sin-cos-mult` `unswap-sqr`

Counts

2 → 33

Calls

2 calls:

24.0ms	(* (sin (/ eps 2)) (cos (fma eps 1/2 x)))
5.0ms	(cos (fma eps 1/2 x))

series95.0ms

Counts

2 → 6

Calls

2 calls:

62.0ms	(* (sin (/ eps 2)) (cos (fma eps 1/2 x)))
33.0ms	(cos (fma eps 1/2 x))

simplify1.0s

Counts

39 → 39

Iterations

Iter	Nodes
done	2000
4	2000
3	880
2	324
1	148
0	74

prune188.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (* eps 1/2)) (cos x))
0.1b	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
0.2b	(* (sin (* eps 1/2)) (sin x))
0.3b	(* (sin (/ eps 2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `insert-posit16` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `prod-diff` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`flip3--` `frac-sub` `flip--` `sub-div`
1×	`fma-neg` `diff-log`

Counts

4 → 94

Calls

4 calls:

31.0ms	(* (cos (* eps 1/2)) (cos x))
54.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
32.0ms	(* (sin (* eps 1/2)) (sin x))
119.0ms	(* (sin (/ eps 2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

series399.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (cos (* eps 1/2)) (cos x))
124.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
89.0ms	(* (sin (* eps 1/2)) (sin x))
136.0ms	(* (sin (/ eps 2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

simplify1.3s

Counts

106 → 106

Iterations

Iter	Nodes
done	2004
3	2004
2	1088
1	398
0	172

prune728.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes199.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	29
2	29
1	27
0	19

end0.0ms

sample7.4s

Algorithm

intervals

Results

3.9s	3303×	body	1280	valid
1.6s	1817×	body	640	valid
1.0s	656×	body	2560	valid
334.0ms	779×	body	320	valid
164.0ms	1081×	body	80	valid
119.0ms	364×	body	160	valid