Details

sample207.0ms

Algorithm

intervals

Results

96.0ms	104×	body	1280	valid
44.0ms	51×	body	640	valid
31.0ms	21×	body	2560	valid
14.0ms	28×	body	320	valid
6.0ms	36×	body	80	valid
5.0ms	16×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize17.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (sin (+ x eps)) (sin x))
3.8b	(sin (+ x eps))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

60.0ms	(- (sin (+ x eps)) (sin x))
51.0ms	(sin (+ x eps))

series96.0ms

Counts

2 → 6

Calls

2 calls:

60.0ms	(- (sin (+ x eps)) (sin x))
36.0ms	(sin (+ x eps))

simplify933.0ms

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
3	1462
2	383
1	137
0	65

prune128.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(/ (+ (+ x eps) x) 2)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.6b	(cos (/ (+ (+ x eps) x) 2))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
18×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
15×	`times-frac` `distribute-lft-out`
9×	`add-log-exp`
8×	`add-cbrt-cube` `add-exp-log`
6×	`pow1`
5×	`associate-/l*`
4×	`insert-posit16`
3×	`associate-/r` `sum-log` `associate-r` `associate-l*`
2×	`flip3-+` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l+` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `div-inv` `sin-cos-mult` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

18.0ms	(+ (+ x eps) x)
47.0ms	(/ (+ (+ x eps) x) 2)
14.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
30.0ms	(cos (/ (+ (+ x eps) x) 2))

series199.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(+ (+ x eps) x)
45.0ms	(/ (+ (+ x eps) x) 2)
74.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
38.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify875.0ms

Counts

94 → 94

Iterations

Iter	Nodes
done	5002
2	1270
1	310
0	137

prune438.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (sin (* eps 1/2)) (cos (+ (* eps 1/2) x)))
3.6b	(cos (+ (* eps 1/2) x))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 29

Calls

2 calls:

26.0ms	(* (sin (* eps 1/2)) (cos (+ (* eps 1/2) x)))
17.0ms	(cos (+ (* eps 1/2) x))

series116.0ms

Counts

2 → 6

Calls

2 calls:

84.0ms	(* (sin (* eps 1/2)) (cos (+ (* eps 1/2) x)))
32.0ms	(cos (+ (* eps 1/2) x))

simplify1.7s

Counts

35 → 35

Iterations

Iter	Nodes
done	5001
3	2775
2	494
1	146
0	70

prune262.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

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

rewrite283.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
6×	`add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`associate-*r/` `insert-posit16`
3×	`sub-neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `frac-sub` `flip--` `sub-div`
1×	`diff-log`

Counts

4 → 82

Calls

4 calls:

33.0ms	(* (cos (* eps 1/2)) (cos x))
51.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
22.0ms	(* (sin (* eps 1/2)) (sin x))
175.0ms	(* (sin (* eps 1/2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(* (cos (* eps 1/2)) (cos x))
139.0ms	(- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x)))
71.0ms	(* (sin (* eps 1/2)) (sin x))
197.0ms	(* (sin (* eps 1/2)) (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))))

simplify1.3s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1668
1	345
0	147

prune481.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes210.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	35
3	35
2	34
1	29
0	16

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.0s	3236×	body	1280	valid
1.5s	1918×	body	640	valid
995.0ms	617×	body	2560	valid
493.0ms	1090×	body	80	valid
438.0ms	766×	body	320	valid
98.0ms	373×	body	160	valid