Details

sample138.0ms

Algorithm

intervals

Results

71.0ms	140×	body	1280	valid
23.0ms	17×	body	2560	valid
20.0ms	60×	body	640	valid
5.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	5×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize61.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite27.0ms

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` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

16.0ms	(- (cos (+ x eps)) (cos x))
8.0ms	(cos (+ x eps))

series122.0ms

Counts

2 → 6

Calls

2 calls:

95.0ms	(- (cos (+ x eps)) (cos x))
28.0ms	(cos (+ x eps))

simplify3.1s

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
4	3416
3	1175
2	423
1	200
0	91

prune297.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize39.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
3.1b	(sin (/ (fma 2 x eps) 2))

rewrite66.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

33.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
26.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series230.0ms

Counts

3 → 9

Calls

3 calls:

90.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2))))
99.0ms	(* (sin (* 1/2 eps)) (sin (/ (fma 2 x eps) 2)))
41.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.6s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	2079
2	599
1	222
0	97

prune439.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* (sin (* eps 1/2)) -2) (sin (fma 1/2 eps x)))
3.1b	(sin (fma 1/2 eps x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `sin-sum` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod` `fma-udef`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative`

Counts

2 → 32

Calls

2 calls:

28.0ms	(* (* (sin (* eps 1/2)) -2) (sin (fma 1/2 eps x)))
2.0ms	(sin (fma 1/2 eps x))

series138.0ms

Counts

2 → 6

Calls

2 calls:

94.0ms	(* (* (sin (* eps 1/2)) -2) (sin (fma 1/2 eps x)))
44.0ms	(sin (fma 1/2 eps x))

simplify2.9s

Counts

38 → 38

Iterations

Iter	Nodes
done	5001
3	1988
2	627
1	194
0	77

prune207.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite108.0ms

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` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `sum-log` `fma-def` `distribute-lft-in`

Counts

4 → 78

Calls

4 calls:

14.0ms	(* (cos x) (sin (* eps 1/2)))
14.0ms	(* (cos (* eps 1/2)) (sin x))
15.0ms	(+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x)))
62.0ms	(* (* (sin (* eps 1/2)) -2) (+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos x) (sin (* eps 1/2)))
65.0ms	(* (cos (* eps 1/2)) (sin x))
159.0ms	(+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x)))
185.0ms	(* (* (sin (* eps 1/2)) -2) (+ (* (cos x) (sin (* eps 1/2))) (* (cos (* eps 1/2)) (sin x))))

simplify1.9s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1967
1	448
0	160

prune688.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes390.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	17
1	17
0	13

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.1s	4431×	body	1280	valid
1.5s	650×	body	2560	valid
927.0ms	1841×	body	640	valid
391.0ms	80×	body	80	valid
288.0ms	743×	body	320	valid
46.0ms	255×	body	160	valid