Details

sample177.0ms

Algorithm

intervals

Results

112.0ms	159×	body	1280	valid
22.0ms	52×	body	640	valid
21.0ms	14×	body	2560	valid
6.0ms	19×	body	320	valid
2.0ms	10×	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: 37.6b

localize46.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.0b	(cos (+ x eps))

rewrite40.0ms

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:

21.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

series89.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (cos (+ x eps)) (cos x))
20.0ms	(cos (+ x eps))

simplify2.2s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	3787
4	1424
3	658
2	282
1	137
0	67

prune205.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
2.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite186.0ms

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:

80.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
11.0ms	(+ x (+ x eps))
68.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
25.0ms	(sin (/ (+ x (+ x eps)) 2))

series307.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(* -2 (* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2))))
43.0ms	(+ x (+ x eps))
105.0ms	(* (sin (* 1/2 eps)) (sin (/ (+ x (+ x eps)) 2)))
53.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5043
3	3226
2	832
1	289
0	121

prune453.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (sin (/ eps 2)))
0.3b	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
2.1b	(sin (+ (/ eps 2) x))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 49

Calls

3 calls:

15.0ms	(* -2 (sin (/ eps 2)))
48.0ms	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
18.0ms	(sin (+ (/ eps 2) x))

series142.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* -2 (sin (/ eps 2)))
82.0ms	(* (* -2 (sin (/ eps 2))) (sin (+ (/ eps 2) x)))
24.0ms	(sin (+ (/ eps 2) x))

simplify2.6s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
3	1988
2	641
1	242
0	100

prune269.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
18×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`-un-lft-identity` `associate-r` `associate-l*` `add-cube-cbrt`
4×	`*-commutative` `insert-posit16` `add-log-exp`
2×	`sin-cos-mult` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 86

Calls

4 calls:

16.0ms	(* (cos (/ eps 2)) (sin x))
18.0ms	(* (sin (/ eps 2)) (cos x))
31.0ms	(* (* (cos (/ eps 2)) (sin x)) (* -2 (sin (/ eps 2))))
53.0ms	(* (* (sin (/ eps 2)) (cos x)) (* -2 (sin (/ eps 2))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (cos (/ eps 2)) (sin x))
61.0ms	(* (sin (/ eps 2)) (cos x))
100.0ms	(* (* (cos (/ eps 2)) (sin x)) (* -2 (sin (/ eps 2))))
71.0ms	(* (* (sin (/ eps 2)) (cos x)) (* -2 (sin (/ eps 2))))

simplify1.5s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	1504
1	417
0	165

prune469.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

regimes214.0ms

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	21
1	21
0	15

end0.0ms

sample6.7s

Algorithm

intervals

Results

4.5s	4425×	body	1280	valid
875.0ms	618×	body	2560	valid
841.0ms	1901×	body	640	valid
232.0ms	711×	body	320	valid
53.0ms	277×	body	160	valid
6.0ms	68×	body	80	valid