Details

sample138.0ms

Algorithm

intervals

Results

54.0ms	98×	body	1280	valid
47.0ms	24×	body	2560	valid
19.0ms	56×	body	640	valid
5.0ms	22×	body	320	valid
3.0ms	44×	body	80	valid
2.0ms	12×	body	160	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: 35.7b

localize13.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.7b	(sin (+ x eps))

rewrite112.0ms

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:

101.0ms	(- (sin (+ x eps)) (sin x))
9.0ms	(sin (+ x eps))

series108.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(- (sin (+ x eps)) (sin x))
37.0ms	(sin (+ x eps))

simplify3.0s

Counts

48 → 48

Iterations

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

prune222.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize36.0ms

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)))
2.8b	(cos (/ (fma 2 x eps) 2))

rewrite71.0ms

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:

45.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
20.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
4.0ms	(cos (/ (fma 2 x eps) 2))

series205.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2))))
69.0ms	(* (sin (/ eps 2)) (cos (/ (fma 2 x eps) 2)))
41.0ms	(cos (/ (fma 2 x eps) 2))

simplify2.2s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2177
2	629
1	235
0	100

prune346.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* (sin (* 1/2 eps)) 2) (cos (fma eps 1/2 x)))
2.8b	(cos (fma eps 1/2 x))

rewrite59.0ms

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×	`cos-sum` `associate-l` `*-commutative` `fma-udef`

Counts

2 → 32

Calls

2 calls:

55.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (fma eps 1/2 x)))
3.0ms	(cos (fma eps 1/2 x))

series122.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(* (* (sin (* 1/2 eps)) 2) (cos (fma eps 1/2 x)))
36.0ms	(cos (fma eps 1/2 x))

simplify4.0s

Counts

38 → 38

Iterations

Iter	Nodes
done	5000
4	4975
3	1656
2	523
1	174
0	74

prune229.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize50.0ms

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

rewrite327.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

18.0ms	(* (cos (* eps 1/2)) (cos x))
56.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
32.0ms	(* (sin (* eps 1/2)) (sin x))
217.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

series501.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (cos (* eps 1/2)) (cos x))
143.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
94.0ms	(* (sin (* eps 1/2)) (sin x))
197.0ms	(* (* (sin (* 1/2 eps)) 2) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

simplify1.9s

Counts

106 → 106

Iterations

Iter	Nodes
done	5001
2	1453
1	456
0	176

prune582.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes169.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	30
2	30
1	28
0	20

end0.0ms

sample5.6s

Algorithm

intervals

Results

2.8s	3263×	body	1280	valid
1.3s	649×	body	2560	valid
903.0ms	1897×	body	640	valid
203.0ms	762×	body	320	valid
96.0ms	336×	body	160	valid
87.0ms	1093×	body	80	valid