Details

sample271.0ms

Algorithm

intervals

Results

153.0ms	129×	body	1280	valid
51.0ms	29×	body	2560	valid
39.0ms	62×	body	640	valid
12.0ms	28×	body	320	valid
2.0ms	6×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize14.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ x eps)) (cos x))
4.1b	(cos (+ x eps))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 26

Calls

2 calls:

12.0ms	(- (cos (+ x eps)) (cos x))
7.0ms	(cos (+ x eps))

series113.0ms

Counts

2 → 6

Calls

2 calls:

70.0ms	(- (cos (+ x eps)) (cos x))
43.0ms	(cos (+ x eps))

simplify1.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	2044
5	2044
4	1424
3	658
2	282
1	137
0	67

prune283.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
4.2b	(sin (/ (+ x (+ x eps)) 2))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt`
6×	`associate-l`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

71.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
22.0ms	(+ x (+ x eps))
96.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
29.0ms	(sin (/ (+ x (+ x eps)) 2))

series244.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
31.0ms	(+ x (+ x eps))
83.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
42.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	2008
3	2008
2	826
1	291
0	123

prune896.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* eps 1/2)) (* -2 (sin (* 1/2 (+ eps (+ x x))))))
4.2b	(sin (* 1/2 (+ eps (+ x x))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

13×	`distribute-rgt-in` `distribute-lft-in`
10×	`sin-sum`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`insert-posit16` `add-log-exp`
1×	`associate-r` `*-commutative`

Counts

2 → 37

Calls

2 calls:

59.0ms	(* (sin (* eps 1/2)) (* -2 (sin (* 1/2 (+ eps (+ x x))))))
16.0ms	(sin (* 1/2 (+ eps (+ x x))))

series169.0ms

Counts

2 → 6

Calls

2 calls:

121.0ms	(* (sin (* eps 1/2)) (* -2 (sin (* 1/2 (+ eps (+ x x))))))
48.0ms	(sin (* 1/2 (+ eps (+ x x))))

simplify957.0ms

Counts

43 → 43

Iterations

Iter	Nodes
done	2001
3	2001
2	666
1	248
0	108

prune523.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

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

rewrite359.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

26.0ms	(* (sin (* eps 1/2)) (cos (* (+ x x) 1/2)))
28.0ms	(* (cos (* eps 1/2)) (sin (* (+ x x) 1/2)))
50.0ms	(+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))
255.0ms	(* (sin (* eps 1/2)) (* -2 (+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))))

series460.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(* (sin (* eps 1/2)) (cos (* (+ x x) 1/2)))
63.0ms	(* (cos (* eps 1/2)) (sin (* (+ x x) 1/2)))
127.0ms	(+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))
198.0ms	(* (sin (* eps 1/2)) (* -2 (+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))))

simplify1.3s

Counts

88 → 88

Iterations

Iter	Nodes
done	2003
3	2003
2	1597
1	455
0	174

prune1.1s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.1b

regimes262.0ms

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	27
1	27
0	18

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.2s	4377×	body	1280	valid
2.1s	1903×	body	640	valid
1.1s	640×	body	2560	valid
356.0ms	714×	body	320	valid
73.0ms	280×	body	160	valid
11.0ms	86×	body	80	valid