Details

sample212.0ms

Algorithm

intervals

Results

128.0ms	159×	body	1280	valid
39.0ms	52×	body	640	valid
23.0ms	14×	body	2560	valid
7.0ms	19×	body	320	valid
3.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

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: 37.6b

localize41.0ms

Local error

Found 2 expressions with local error:

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

rewrite36.0ms

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:

23.0ms	(- (cos (+ x eps)) (cos x))
11.0ms	(cos (+ x eps))

series127.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (cos (+ x eps)) (cos x))
41.0ms	(cos (+ x eps))

simplify3.3s

Counts

32 → 32

Iterations

Iter	Nodes
done	5000
5	4923
4	1856
3	763
2	290
1	137
0	67

prune197.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite149.0ms

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:

56.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
16.0ms	(+ x (+ x eps))
55.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
22.0ms	(sin (/ (+ x (+ x eps)) 2))

series242.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2))))
25.0ms	(+ x (+ x eps))
79.0ms	(* (sin (/ eps 2)) (sin (/ (+ x (+ x eps)) 2)))
42.0ms	(sin (/ (+ x (+ x eps)) 2))

simplify2.3s

Counts

76 → 76

Iterations

Iter	Nodes
done	5002
3	3959
2	868
1	291
0	123

prune391.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (* -2 (sin (+ (/ eps 2) x))) (sin (/ eps 2)))
2.1b	(sin (+ (/ 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×	`sin-sum` `associate-l` `*-commutative`

Counts

2 → 28

Calls

2 calls:

65.0ms	(* (* -2 (sin (+ (/ eps 2) x))) (sin (/ eps 2)))
19.0ms	(sin (+ (/ eps 2) x))

series119.0ms

Counts

2 → 6

Calls

2 calls:

72.0ms	(* (* -2 (sin (+ (/ eps 2) x))) (sin (/ eps 2)))
46.0ms	(sin (+ (/ eps 2) x))

simplify2.0s

Counts

34 → 34

Iterations

Iter	Nodes
done	5000
3	1968
2	486
1	172
0	75

prune239.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize65.0ms

Local error

Found 4 expressions with local error:

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

rewrite132.0ms

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`
4×	`insert-posit16`
3×	`*-commutative`
2×	`flip3-+` `associate-l/` `associate-r/` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log` `sin-cos-mult`

Counts

4 → 72

Calls

4 calls:

17.0ms	(* (cos (/ eps 2)) (sin x))
26.0ms	(+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x)))
13.0ms	(* (sin (/ eps 2)) (cos x))
73.0ms	(* (* -2 (+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x)))) (sin (/ eps 2)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos (/ eps 2)) (sin x))
137.0ms	(+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x)))
84.0ms	(* (sin (/ eps 2)) (cos x))
183.0ms	(* (* -2 (+ (* (sin (/ eps 2)) (cos x)) (* (cos (/ eps 2)) (sin x)))) (sin (/ eps 2)))

simplify1.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1561
1	418
0	160

prune520.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes243.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	22
1	22
0	18

end0.0ms

sample8.1s

Algorithm

intervals

Results

4.8s	4425×	body	1280	valid
1.3s	1901×	body	640	valid
1.1s	618×	body	2560	valid
700.0ms	711×	body	320	valid
115.0ms	277×	body	160	valid
9.0ms	68×	body	80	valid