Details

sample154.0ms

Algorithm

intervals

Results

83.0ms	143×	body	1280	valid
29.0ms	22×	body	2560	valid
16.0ms	45×	body	640	valid
8.0ms	30×	body	320	valid
2.0ms	14×	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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.0b

localize24.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite381.0ms

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`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

14.0ms	(- (cos (+ x eps)) (cos x))
367.0ms	(cos (+ x eps))

series117.0ms

Counts

2 → 6

Calls

2 calls:

98.0ms	(- (cos (+ x eps)) (cos x))
19.0ms	(cos (+ x eps))

simplify2.5s

Counts

30 → 30

Iterations

Iter	Nodes
done	5015
5	4022
4	1465
3	652
2	280
1	135
0	65

prune220.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.4b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
0.0b	(+ x (+ x eps))
0.3b	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
3.0b	(sin (/ (+ x (+ x eps)) 2))

rewrite229.0ms

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`
3×	`sum-log` `distribute-lft-out`
2×	`*-commutative` `sin-mult`
1×	`+-commutative` `associate-+r+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

89.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
12.0ms	(+ x (+ x eps))
82.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
43.0ms	(sin (/ (+ x (+ x eps)) 2))

series352.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
28.0ms	(+ x (+ x eps))
143.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
54.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.9s

Counts

72 → 72

Iterations

Iter	Nodes
done	5000
3	3797
2	858
1	287
0	118

prune548.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (+ (* eps 1/2) x))) (sin (* eps 1/2)))
3.0b	(sin (+ (* eps 1/2) x))

rewrite119.0ms

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×	`add-log-exp`
1×	`sin-sum` `associate-l` `*-commutative`

Counts

2 → 26

Calls

2 calls:

95.0ms	(* (* -2 (sin (+ (* eps 1/2) x))) (sin (* eps 1/2)))
22.0ms	(sin (+ (* eps 1/2) x))

series125.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(* (* -2 (sin (+ (* eps 1/2) x))) (sin (* eps 1/2)))
32.0ms	(sin (+ (* eps 1/2) x))

simplify2.8s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
3	1456
2	457
1	166
0	73

prune239.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite184.0ms

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` `cbrt-unprod`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `sin-cos-mult`

Counts

4 → 68

Calls

4 calls:

25.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
16.0ms	(* (cos (* eps 1/2)) (sin x))
16.0ms	(* (sin (* eps 1/2)) (cos x))
126.0ms	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
64.0ms	(* (cos (* eps 1/2)) (sin x))
70.0ms	(* (sin (* eps 1/2)) (cos x))
200.0ms	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

simplify2.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5000
2	1660
1	416
0	156

prune557.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes411.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	24
1	24
0	17

end0.0ms

sample6.6s

Algorithm

intervals

Results

3.8s	4444×	body	1280	valid
1.3s	1858×	body	640	valid
947.0ms	655×	body	2560	valid
267.0ms	708×	body	320	valid
59.0ms	260×	body	160	valid
7.0ms	75×	body	80	valid