Details

sample149.0ms

Algorithm

intervals

Results

68.0ms	113×	body	1280	valid
28.0ms	21×	body	2560	valid
28.0ms	54×	body	640	valid
6.0ms	26×	body	320	valid
3.0ms	30×	body	80	valid
2.0ms	12×	body	160	valid

simplify5.0ms

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: 41.6b

localize12.0ms

Local error

Found 2 expressions with local error:

1.8b	(- (sin (+ x eps)) (sin x))
3.6b	(sin (+ x eps))

rewrite103.0ms

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:

83.0ms	(- (sin (+ x eps)) (sin x))
18.0ms	(sin (+ x eps))

series80.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(- (sin (+ x eps)) (sin x))
27.0ms	(sin (+ x eps))

simplify941.0ms

Counts

30 → 30

Iterations

Useful iterations: done (940.0ms)

Iter	Nodes	Cost
0	64	309
1	135	295
2	381	281
3	1453	275
done	5000	271

prune135.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.3b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-log-exp`
7×	`add-sqr-sqrt`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sum-log` `distribute-lft-out`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `prod-exp` `*-commutative` `sin-cos-mult` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

3 → 41

Calls

3 calls:

30.0ms	(+ (+ x eps) x)
31.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
66.0ms	(cos (/ (+ (+ x eps) x) 2))

series133.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(+ (+ x eps) x)
82.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
27.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify706.0ms

Counts

50 → 50

Iterations

Useful iterations: done (705.0ms)

Iter	Nodes	Cost
0	91	656
1	219	646
2	982	568
done	5000	552

prune240.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.3b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
0.4b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `*-un-lft-identity`
9×	`log-prod` `exp-prod`
8×	`pow1` `log-pow`
7×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `associate-l`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 61

Calls

4 calls:

68.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
93.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
116.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
69.0ms	(cos (/ (+ (+ x eps) x) 2))

series235.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
89.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
26.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
39.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify3.9s

Counts

73 → 73

Iterations

Useful iterations: 3 (979.0ms)

Iter	Nodes	Cost
0	107	1191
1	227	1093
2	807	951
3	4205	931
done	5000	931

prune340.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
0.5b	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
0.6b	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
3.5b	(cos (/ (+ (+ x eps) x) 2))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

31.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
5.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
7.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
91.0ms	(cos (/ (+ (+ x eps) x) 2))

series264.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (sin (/ eps 2)) (cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3)))
52.0ms	(cbrt (pow (cos (/ (+ (+ x eps) x) 2)) 3))
85.0ms	(pow (cos (/ (+ (+ x eps) x) 2)) 3)
39.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

97 → 97

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	117	1733
1	299	1463
2	1825	1279
done	5001	1263

prune399.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.2b

regimes205.0ms

Accuracy

99.3% (0.1b remaining)

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

bsearch205.0ms

Steps

Iters	Range		Point
9	1.3016113514811783e-15	5.2366538615162886e-09	5.156835808069301e-09
8	-0.03117879455470207	-2.7237372521413145e-05	-2.7541666583250866e-05

simplify8.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	25	51
1	35	38
done	35	38

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.7s	3317×	body	1280	valid
988.0ms	647×	body	2560	valid
931.0ms	1861×	body	640	valid
207.0ms	734×	body	320	valid
91.0ms	1080×	body	80	valid
71.0ms	361×	body	160	valid