Details

sample146.0ms

Algorithm

intervals

Results

78.0ms	140×	body	1280	valid
23.0ms	17×	body	2560	valid
22.0ms	60×	body	640	valid
6.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	5×	body	80	valid

simplify4.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.8b	(- (cos (+ x eps)) (cos x))
3.2b	(cos (+ x eps))

rewrite57.0ms

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:

40.0ms	(- (cos (+ x eps)) (cos x))
16.0ms	(cos (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (cos (+ x eps)) (cos x))
23.0ms	(cos (+ x eps))

simplify2.7s

Counts

30 → 30

Iterations

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

prune234.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize28.0ms

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)))
3.1b	(sin (/ (+ x (+ x eps)) 2))

rewrite240.0ms

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:

95.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
25.0ms	(+ x (+ x eps))
74.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
43.0ms	(sin (/ (+ x (+ x eps)) 2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(* -2 (* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2))))
25.0ms	(+ x (+ x eps))
91.0ms	(* (sin (/ (+ x (+ x eps)) 2)) (sin (/ eps 2)))
42.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.8s

Counts

72 → 72

Iterations

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

prune356.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (+ (* eps 1/2) x))) (sin (* eps 1/2)))
3.1b	(sin (+ (* eps 1/2) x))

rewrite80.0ms

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:

67.0ms	(* (* -2 (sin (+ (* eps 1/2) x))) (sin (* eps 1/2)))
12.0ms	(sin (+ (* eps 1/2) x))

series131.0ms

Counts

2 → 6

Calls

2 calls:

106.0ms	(* (* -2 (sin (+ (* eps 1/2) x))) (sin (* eps 1/2)))
25.0ms	(sin (+ (* eps 1/2) x))

simplify2.6s

Counts

32 → 32

Iterations

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

prune295.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sin (* eps 1/2)) (cos x))
0.2b	(* (cos (* eps 1/2)) (sin x))
0.2b	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
0.3b	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

rewrite282.0ms

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:

30.0ms	(* (sin (* eps 1/2)) (cos x))
30.0ms	(* (cos (* eps 1/2)) (sin x))
41.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
178.0ms	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (sin (* eps 1/2)) (cos x))
62.0ms	(* (cos (* eps 1/2)) (sin x))
137.0ms	(+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))
217.0ms	(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))

simplify1.8s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
2	1631
1	416
0	156

prune455.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes230.0ms

Accuracy

0% (0.9b remaining)

Error of 1.0b against oracle of 0.1b and baseline of 1.0b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	24
1	24
0	17

end0.0ms

sample6.7s

Algorithm

intervals

Results

3.5s	4431×	body	1280	valid
1.5s	650×	body	2560	valid
899.0ms	1841×	body	640	valid
313.0ms	743×	body	320	valid
45.0ms	255×	body	160	valid
8.0ms	80×	body	80	valid