Details

sample194.0ms

Algorithm

intervals

Results

75.0ms	96×	body	1280	valid
40.0ms	24×	body	2560	valid
31.0ms	38×	body	320	valid
27.0ms	56×	body	640	valid
3.0ms	31×	body	80	valid
3.0ms	11×	body	160	valid

simplify3.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite84.0ms

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:

66.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

series78.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(- (sin (+ x eps)) (sin x))
23.0ms	(sin (+ x eps))

simplify2.5s

Counts

30 → 30

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	64	309
1	189	295
2	995	277
done	5001	273

prune138.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* (sin (/ (- eps 0) 2)) (cos (/ (+ (+ x eps) x) 2))))
0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ (- eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
6.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite241.0ms

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:

74.0ms	(* 2 (* (sin (/ (- eps 0) 2)) (cos (/ (+ (+ x eps) x) 2))))
53.0ms	(+ (+ x eps) x)
39.0ms	(* (sin (/ (- eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
73.0ms	(cos (/ (+ (+ x eps) x) 2))

series222.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* 2 (* (sin (/ (- eps 0) 2)) (cos (/ (+ (+ x eps) x) 2))))
36.0ms	(+ (+ x eps) x)
77.0ms	(* (sin (/ (- eps 0) 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.0s

Counts

72 → 72

Iterations

Useful iterations: done (999.0ms)

Iter	Nodes	Cost
0	120	1202
1	590	1077
done	5000	913

prune284.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize37.0ms

Local error

Found 3 expressions with local error:

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

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-r` `*-commutative` `flip-+`

Counts

3 → 40

Calls

3 calls:

29.0ms	(+ (+ x eps) x)
36.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (* (sin (/ eps 2)) 2))
47.0ms	(cos (/ (+ (+ x eps) x) 2))

series178.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(+ (+ x eps) x)
98.0ms	(* (cos (/ (+ (+ x eps) x) 2)) (* (sin (/ eps 2)) 2))
31.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify4.8s

Counts

49 → 49

Iterations

Useful iterations: done (4.8s)

Iter	Nodes	Cost
0	91	690
1	387	672
2	3699	556
done	5000	548

prune219.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)) (* (sin (/ eps 2)) 2))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.5b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
6.1b	(cos (/ (+ (+ x eps) x) 2))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
15×	`associate-l`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`pow1` `add-exp-log`
9×	`unpow-prod-down` `cube-prod`
8×	`add-cbrt-cube`
4×	`add-log-exp`
3×	`cube-mult` `pow-unpow` `unpow3` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `pow1/3` `associate-r` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

47.0ms	(* (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)) (* (sin (/ eps 2)) 2))
3.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
9.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
71.0ms	(cos (/ (+ (+ x eps) x) 2))

series287.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)) (* (sin (/ eps 2)) 2))
42.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
71.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
29.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.6s

Counts

93 → 93

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	116	1639
1	742	1309
done	5000	1219

prune331.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes164.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 14.8b

bsearch236.0ms

Steps

Iters	Range		Point
11	1.1123901126486127e-34	1.9762467893330864e-06	9.433852813731428e-09
9	-108.09236434424712	-9.640722949014248e-05	-9.760584355965869e-05

simplify8.0ms

Iterations

Useful iterations: done (8.0ms)

Iter	Nodes	Cost
0	29	53
1	39	53
done	39	51

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.3s	3267×	body	1280	valid
1.6s	1788×	body	640	valid
914.0ms	640×	body	2560	valid
457.0ms	834×	body	320	valid
158.0ms	1105×	body	80	valid
131.0ms	366×	body	160	valid