Details

sample189.0ms

Algorithm

intervals

Results

91.0ms	105×	body	1280	valid
41.0ms	75×	body	640	valid
28.0ms	16×	body	2560	valid
5.0ms	15×	body	320	valid
4.0ms	32×	body	80	valid
3.0ms	13×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune256.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize31.0ms

Local error

Found 2 expressions with local error:

1.5b	(- (sin (+ x eps)) (sin x))
4.5b	(sin (+ x eps))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
4×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `sin-sum` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

109.0ms	(- (sin (+ x eps)) (sin x))
20.0ms	(sin (+ x eps))

series100.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (sin (+ x eps)) (sin x))
32.0ms	(sin (+ x eps))

simplify10.3s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3859
3	1264
2	445
1	202
0	91

prune324.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
4.6b	(cos (/ (fma 2 x eps) 2))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

38.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
16.0ms	(cos (/ (fma 2 x eps) 2))

series157.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(* (sin (* 1/2 eps)) (cos (/ (fma 2 x eps) 2)))
58.0ms	(cos (/ (fma 2 x eps) 2))

simplify7.5s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
4	2909
3	1026
2	356
1	148
0	66

prune413.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* 1/2 eps)) (cos (fma eps 1/2 x)))
4.6b	(cos (fma eps 1/2 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 31

Calls

2 calls:

30.0ms	(* (sin (* 1/2 eps)) (cos (fma eps 1/2 x)))
5.0ms	(cos (fma eps 1/2 x))

series209.0ms

Counts

2 → 6

Calls

2 calls:

170.0ms	(* (sin (* 1/2 eps)) (cos (fma eps 1/2 x)))
39.0ms	(cos (fma eps 1/2 x))

simplify3.9s

Counts

37 → 37

Iterations

Iter	Nodes
done	5000
4	2345
3	879
2	325
1	144
0	69

prune448.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize76.0ms

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

rewrite554.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `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 → 90

Calls

4 calls:

36.0ms	(* (cos (* eps 1/2)) (cos x))
110.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
34.0ms	(* (sin (* eps 1/2)) (sin x))
357.0ms	(* (sin (* 1/2 eps)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

series614.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (cos (* eps 1/2)) (cos x))
169.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
134.0ms	(* (sin (* eps 1/2)) (sin x))
225.0ms	(* (sin (* 1/2 eps)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

simplify5.5s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4568
2	1377
1	396
0	166

prune1.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes354.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample11.1s

Algorithm

intervals

Results

5.9s	3290×	body	1280	valid
2.2s	1849×	body	640	valid
1.9s	646×	body	2560	valid
473.0ms	737×	body	320	valid
232.0ms	1140×	body	80	valid
91.0ms	338×	body	160	valid