Details

sample149.0ms

Algorithm

intervals

Results

94.0ms	137×	body	1280	valid
19.0ms	68×	body	640	valid
16.0ms	15×	body	2560	valid
4.0ms	24×	body	320	valid
1.0ms	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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.8b

localize15.0ms

Local error

Found 2 expressions with local error:

1.0b	(- (cos (+ eps x)) (cos x))
3.8b	(cos (+ eps x))

rewrite21.0ms

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:

11.0ms	(- (cos (+ eps x)) (cos x))
9.0ms	(cos (+ eps x))

series103.0ms

Counts

2 → 6

Calls

2 calls:

86.0ms	(- (cos (+ eps x)) (cos x))
18.0ms	(cos (+ eps x))

simplify611.0ms

Counts

30 → 30

Iterations

Iter	Nodes
done	5001
3	1148
2	352
1	131
0	65

prune214.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2))))
0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
3.9b	(sin (/ (+ (+ x eps) x) 2))

rewrite319.0ms

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-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

127.0ms	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2))))
42.0ms	(+ (+ x eps) x)
110.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
38.0ms	(sin (/ (+ (+ x eps) x) 2))

series327.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(* -2 (* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2))))
42.0ms	(+ (+ x eps) x)
95.0ms	(* (sin (/ (+ (+ x eps) x) 2)) (sin (/ eps 2)))
51.0ms	(sin (/ (+ (+ x eps) x) 2))

simplify581.0ms

Counts

72 → 72

Iterations

Iter	Nodes
done	5001
2	1165
1	286
0	118

prune505.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (sin (* eps 1/2)) (* -2 (sin (+ x (* eps 1/2)))))
3.9b	(sin (+ x (* eps 1/2)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`sin-sum`
4×	`distribute-rgt-in` `distribute-lft-in`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`add-log-exp`
1×	`associate-r` `*-commutative`

Counts

2 → 30

Calls

2 calls:

57.0ms	(* (sin (* eps 1/2)) (* -2 (sin (+ x (* eps 1/2)))))
15.0ms	(sin (+ x (* eps 1/2)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(* (sin (* eps 1/2)) (* -2 (sin (+ x (* eps 1/2)))))
29.0ms	(sin (+ x (* eps 1/2)))

simplify1.5s

Counts

36 → 36

Iterations

Iter	Nodes
done	5001
3	2726
2	652
1	191
0	82

prune260.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite152.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `pow1` `add-cbrt-cube` `add-exp-log`
9×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/`
3×	`*-commutative`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`+-commutative` `sum-log`

Counts

4 → 71

Calls

4 calls:

14.0ms	(* (cos (* 1/2 eps)) (sin x))
22.0ms	(+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))
22.0ms	(* (cos x) (sin (* 1/2 eps)))
93.0ms	(* (sin (* eps 1/2)) (* -2 (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))))

series489.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (cos (* 1/2 eps)) (sin x))
139.0ms	(+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))
78.0ms	(* (cos x) (sin (* 1/2 eps)))
216.0ms	(* (sin (* eps 1/2)) (* -2 (+ (* (cos (* 1/2 eps)) (sin x)) (* (cos x) (sin (* 1/2 eps))))))

simplify997.0ms

Counts

83 → 83

Iterations

Iter	Nodes
done	5000
2	2055
1	430
0	164

prune593.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes242.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	24
1	24
0	16

end0.0ms

sample6.6s

Algorithm

intervals

Results

4.0s	4429×	body	1280	valid
1.1s	656×	body	2560	valid
857.0ms	1835×	body	640	valid
210.0ms	704×	body	320	valid
88.0ms	285×	body	160	valid
8.0ms	91×	body	80	valid