Details

sample185.0ms

Algorithm

intervals

Results

86.0ms	126×	body	1280	valid
51.0ms	69×	body	640	valid
27.0ms	20×	body	2560	valid
9.0ms	25×	body	320	valid
2.0ms	11×	body	160	valid
1.0ms	5×	body	80	valid

simplify6.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.6b

localize27.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
4.3b	(cos (+ x eps))

rewrite72.0ms

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:

26.0ms	(- (cos (+ x eps)) (cos x))
44.0ms	(cos (+ x eps))

series115.0ms

Counts

2 → 6

Calls

2 calls:

83.0ms	(- (cos (+ x eps)) (cos x))
32.0ms	(cos (+ x eps))

simplify1.2s

Counts

32 → 32

Iterations

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

prune337.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize36.0ms

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))

rewrite172.0ms

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:

68.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
12.0ms	(+ x (+ x eps))
68.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
24.0ms	(sin (/ (+ x (+ x eps)) 2))

series242.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
32.0ms	(+ x (+ x eps))
70.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
49.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify1.0s

Counts

76 → 76

Iterations

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

prune781.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize22.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* eps 1/2)) (* -2 (sin (* 1/2 (+ eps (+ x x))))))
4.3b	(sin (* 1/2 (+ eps (+ x x))))

rewrite64.0ms

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:

55.0ms	(* (sin (* eps 1/2)) (* -2 (sin (* 1/2 (+ eps (+ x x))))))
9.0ms	(sin (* 1/2 (+ eps (+ x x))))

series141.0ms

Counts

2 → 6

Calls

2 calls:

99.0ms	(* (sin (* eps 1/2)) (* -2 (sin (* 1/2 (+ eps (+ x x))))))
43.0ms	(sin (* 1/2 (+ eps (+ x x))))

simplify984.0ms

Counts

43 → 43

Iterations

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

prune529.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite477.0ms

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:

74.0ms	(+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))
37.0ms	(* (cos (* eps 1/2)) (sin (* (+ x x) 1/2)))
39.0ms	(* (sin (* eps 1/2)) (cos (* (+ x x) 1/2)))
325.0ms	(* (sin (* eps 1/2)) (* -2 (+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))))

series533.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))
83.0ms	(* (cos (* eps 1/2)) (sin (* (+ x x) 1/2)))
95.0ms	(* (sin (* eps 1/2)) (cos (* (+ x x) 1/2)))
215.0ms	(* (sin (* eps 1/2)) (* -2 (+ (* (sin (* eps 1/2)) (cos (* (+ x x) 1/2))) (* (cos (* eps 1/2)) (sin (* (+ x x) 1/2))))))

simplify1.5s

Counts

88 → 88

Iterations

Iter	Nodes
done	2005
3	2005
2	1599
1	455
0	174

prune1.1s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.0b

regimes233.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	23
1	23
0	16

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.7s	4500×	body	1280	valid
1.6s	1823×	body	640	valid
1.1s	633×	body	2560	valid
338.0ms	685×	body	320	valid
119.0ms	276×	body	160	valid
11.0ms	83×	body	80	valid