Details

sample204.0ms

Algorithm

intervals

Results

78.0ms	96×	body	1280	valid
55.0ms	56×	body	640	valid
33.0ms	24×	body	2560	valid
14.0ms	38×	body	320	valid
3.0ms	31×	body	80	valid
3.0ms	11×	body	160	valid

simplify8.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	7
1	9	7
2	10	7
done	10	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize18.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
6.1b	(sin (+ x eps))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sin-sum` `add-cbrt-cube`
1×	`sub-neg` `flip3--` `diff-log` `diff-sin` `associate--l+` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 24

Calls

2 calls:

100.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

63.0ms	(- (sin (+ x eps)) (sin x))
25.0ms	(sin (+ x eps))

simplify2.8s

Counts

30 → 30

Iterations

Useful iterations: 4 (443.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	284	281
3	572	275
4	1162	271
5	2763	271
done	5000	271

prune71.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
6.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
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-cos-mult`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-*r/` `flip-+` `unswap-sqr`

Counts

4 → 60

Calls

4 calls:

48.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
45.0ms	(+ (+ x eps) x)
27.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
53.0ms	(cos (/ (+ (+ x eps) x) 2))

series218.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
29.0ms	(+ (+ x eps) x)
69.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
40.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.2s

Counts

72 → 72

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	118	1100
1	292	1077
2	819	917
3	2476	893
done	5000	885

prune214.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (cos (+ x (* 1/2 eps))) (* 2 (sin (* 1/2 eps))))
6.1b	(cos (+ x (* 1/2 eps)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 26

Calls

2 calls:

44.0ms	(* (cos (+ x (* 1/2 eps))) (* 2 (sin (* 1/2 eps))))
14.0ms	(cos (+ x (* 1/2 eps)))

series111.0ms

Counts

2 → 6

Calls

2 calls:

89.0ms	(* (cos (+ x (* 1/2 eps))) (* 2 (sin (* 1/2 eps))))
22.0ms	(cos (+ x (* 1/2 eps)))

simplify9.1s

Counts

32 → 32

Iterations

Useful iterations: 3 (494.0ms)

Iter	Nodes	Cost
0	63	480
1	153	467
2	457	381
3	1366	377
4	2654	377
5	4809	377
done	5001	377

prune133.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite317.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
7×	`associate-r`
6×	`add-log-exp`
5×	`pow-prod-down` `prod-exp` `cos-mult` `cbrt-unprod` `sin-mult`
4×	`associate-*l/`
3×	`*-commutative`
2×	`flip3--` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `diff-log`

Counts

4 → 74

Calls

4 calls:

37.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
36.0ms	(* (cos x) (cos (* 1/2 eps)))
40.0ms	(* (sin x) (sin (* 1/2 eps)))
203.0ms	(* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (* 2 (sin (* 1/2 eps))))

series426.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps))))
50.0ms	(* (cos x) (cos (* 1/2 eps)))
63.0ms	(* (sin x) (sin (* 1/2 eps)))
204.0ms	(* (- (* (cos x) (cos (* 1/2 eps))) (* (sin x) (sin (* 1/2 eps)))) (* 2 (sin (* 1/2 eps))))

simplify3.2s

Counts

86 → 86

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	143	1594
1	352	1536
2	1128	1346
3	4279	1292
done	5001	1282

prune345.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes124.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	25
1	22	25
done	22	25

end0.0ms

sample6.0s

Algorithm

intervals

Results

2.7s	3267×	body	1280	valid
1.3s	1788×	body	640	valid
802.0ms	640×	body	2560	valid
428.0ms	366×	body	160	valid
283.0ms	834×	body	320	valid
88.0ms	1105×	body	80	valid