Details

sample175.0ms

Algorithm

intervals

Results

87.0ms	96×	body	1280	valid
30.0ms	24×	body	2560	valid
24.0ms	56×	body	640	valid
13.0ms	38×	body	320	valid
3.0ms	31×	body	80	valid
2.0ms	11×	body	160	valid

simplify4.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.0b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite73.0ms

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:

62.0ms	(- (sin (+ x eps)) (sin x))
10.0ms	(sin (+ x eps))

series88.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(- (sin (+ x eps)) (sin x))
33.0ms	(sin (+ x eps))

simplify2.4s

Counts

30 → 30

Iterations

Useful iterations: 4 (369.0ms)

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

prune97.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize17.0ms

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))

rewrite157.0ms

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:

52.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
26.0ms	(+ (+ x eps) x)
20.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
56.0ms	(cos (/ (+ (+ x eps) x) 2))

series231.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(* 2 (* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2))))
26.0ms	(+ (+ x eps) x)
72.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
41.0ms	(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

prune205.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 3 expressions with local error:

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

rewrite147.0ms

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-r` `pow-prod-down` `prod-exp` `sum-log` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 40

Calls

3 calls:

29.0ms	(+ (+ x eps) x)
53.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (+ (+ x eps) x) 2)))
63.0ms	(cos (/ (+ (+ x eps) x) 2))

series123.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (+ x eps) x)
63.0ms	(* (* 2 (sin (/ eps 2))) (cos (/ (+ (+ x eps) x) 2)))
30.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

49 → 49

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	93	691
1	240	673
2	749	561
3	2306	543
done	5000	537

prune194.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod`
15×	`associate-r`
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-l` `pow-exp` `*-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

45.0ms	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
6.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
45.0ms	(cos (/ (+ (+ x eps) x) 2))

series250.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* (* 2 (sin (/ eps 2))) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
30.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
98.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
44.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify1.4s

Counts

93 → 93

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	121	1649
1	284	1375
2	911	1195
done	5000	1173

prune319.0ms

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

bsearch202.0ms

Steps

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

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	51
1	35	51
done	35	51

end0.0ms

sample5.8s

Algorithm

intervals

Results

2.5s	3267×	body	1280	valid
1.2s	1788×	body	640	valid
1.0s	640×	body	2560	valid
615.0ms	834×	body	320	valid
117.0ms	1105×	body	80	valid
83.0ms	366×	body	160	valid