Details

sample202.0ms

Algorithm

intervals

Results

92.0ms	98×	body	1280	valid
45.0ms	24×	body	2560	valid
33.0ms	56×	body	640	valid
9.0ms	22×	body	320	valid
5.0ms	44×	body	80	valid
3.0ms	12×	body	160	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: 35.7b

localize56.0ms

Local error

Found 2 expressions with local error:

2.0b	(- (sin (+ x eps)) (sin x))
2.7b	(sin (+ x eps))

rewrite65.0ms

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:

49.0ms	(- (sin (+ x eps)) (sin x))
15.0ms	(sin (+ x eps))

series93.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(- (sin (+ x eps)) (sin x))
24.0ms	(sin (+ x eps))

simplify2.7s

Counts

32 → 32

Iterations

Iter	Nodes
done	5001
5	4407
4	1723
3	751
2	308
1	137
0	65

prune127.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2))))
0.0b	(+ x (+ x eps))
0.2b	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
2.8b	(cos (/ (+ x (+ x eps)) 2))

rewrite169.0ms

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-cos-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

81.0ms	(* 2 (* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2))))
15.0ms	(+ x (+ x eps))
31.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
40.0ms	(cos (/ (+ x (+ x eps)) 2))

series214.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(* 2 (* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2))))
26.0ms	(+ x (+ x eps))
53.0ms	(* (sin (* 1/2 eps)) (cos (/ (+ x (+ x eps)) 2)))
41.0ms	(cos (/ (+ x (+ x eps)) 2))

simplify2.9s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	4195
2	910
1	303
0	120

prune417.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* 2 (sin (/ eps 2))) (cos (+ (/ eps 2) x)))
2.8b	(cos (+ (/ eps 2) x))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 28

Calls

2 calls:

62.0ms	(* (* 2 (sin (/ eps 2))) (cos (+ (/ eps 2) x)))
22.0ms	(cos (+ (/ eps 2) x))

series106.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(* (* 2 (sin (/ eps 2))) (cos (+ (/ eps 2) x)))
35.0ms	(cos (+ (/ eps 2) x))

simplify2.7s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	1674
2	476
1	173
0	72

prune203.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite160.0ms

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` `cos-mult` `cbrt-unprod` `sin-mult`
4×	`associate-*r/` `insert-posit16`
3×	`sub-neg` `*-commutative`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`diff-log`

Counts

4 → 82

Calls

4 calls:

18.0ms	(* (cos (/ eps 2)) (cos x))
19.0ms	(- (* (cos (/ eps 2)) (cos x)) (* (sin (/ eps 2)) (sin x)))
15.0ms	(* (sin (/ eps 2)) (sin x))
105.0ms	(* (* 2 (sin (/ eps 2))) (- (* (cos (/ eps 2)) (cos x)) (* (sin (/ eps 2)) (sin x))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos (/ eps 2)) (cos x))
133.0ms	(- (* (cos (/ eps 2)) (cos x)) (* (sin (/ eps 2)) (sin x)))
64.0ms	(* (sin (/ eps 2)) (sin x))
188.0ms	(* (* 2 (sin (/ eps 2))) (- (* (cos (/ eps 2)) (cos x)) (* (sin (/ eps 2)) (sin x))))

simplify1.7s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	1282
1	407
0	156

prune516.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes213.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	40
3	40
2	33
1	27
0	15

end0.0ms

sample6.4s

Algorithm

intervals

Results

3.2s	3263×	body	1280	valid
1.6s	1897×	body	640	valid
925.0ms	649×	body	2560	valid
274.0ms	762×	body	320	valid
145.0ms	336×	body	160	valid
107.0ms	1093×	body	80	valid