Details

sample215.0ms

Algorithm

intervals

Results

81.0ms	97×	body	1280	valid
47.0ms	26×	body	2560	valid
34.0ms	62×	body	640	valid
24.0ms	38×	body	80	valid
9.0ms	26×	body	320	valid
2.0ms	7×	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize23.0ms

Local error

Found 2 expressions with local error:

1.2b	(- (sin (+ x eps)) (sin x))
2.9b	(sin (+ x eps))

rewrite140.0ms

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:

119.0ms	(- (sin (+ x eps)) (sin x))
19.0ms	(sin (+ x eps))

series100.0ms

Counts

2 → 6

Calls

2 calls:

64.0ms	(- (sin (+ x eps)) (sin x))
36.0ms	(sin (+ x eps))

simplify892.0ms

Counts

30 → 30

Iterations

Useful iterations: done (891.0ms)

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

prune102.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ x eps) x)
0.2b	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
3.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite122.0ms

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:

48.0ms	(+ (+ x eps) x)
28.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
45.0ms	(cos (/ (+ (+ x eps) x) 2))

series159.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(+ (+ x eps) x)
77.0ms	(* (sin (/ eps 2)) (cos (/ (+ (+ x eps) x) 2)))
41.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify499.0ms

Counts

50 → 50

Iterations

Useful iterations: done (497.0ms)

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

prune287.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (cos (/ (+ (+ x eps) x) 2)))
0.2b	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
0.5b	(log (exp (cos (/ (+ (+ x eps) x) 2))))
3.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite296.0ms

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:

48.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
85.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
101.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
60.0ms	(cos (/ (+ (+ x eps) x) 2))

series175.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(exp (cos (/ (+ (+ x eps) x) 2)))
52.0ms	(* (sin (/ eps 2)) (log (exp (cos (/ (+ (+ x eps) x) 2)))))
32.0ms	(log (exp (cos (/ (+ (+ x eps) x) 2))))
31.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.6s

Counts

73 → 73

Iterations

Useful iterations: 3 (705.0ms)

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

prune276.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.8b	(log (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
0.8b	(log (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
3.0b	(cos (/ (+ (+ x eps) x) 2))
3.0b	(cos (/ (+ (+ x eps) x) 2))

rewrite257.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod` `log-pow`
10×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `sqrt-pow1`
6×	`add-exp-log` `exp-prod` `sqrt-prod`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow1/2` `rem-log-exp`

Counts

4 → 54

Calls

4 calls:

77.0ms	(log (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
70.0ms	(log (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
39.0ms	(cos (/ (+ (+ x eps) x) 2))
68.0ms	(cos (/ (+ (+ x eps) x) 2))

series237.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(log (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
88.0ms	(log (sqrt (exp (cos (/ (+ (+ x eps) x) 2)))))
25.0ms	(cos (/ (+ (+ x eps) x) 2))
28.0ms	(cos (/ (+ (+ x eps) x) 2))

simplify2.1s

Counts

66 → 66

Iterations

Useful iterations: 3 (131.0ms)

Iter	Nodes	Cost
0	68	976
1	117	916
2	238	812
3	702	796
4	2966	796
done	5001	796

prune507.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 0.5b

regimes219.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 15.1b

bsearch222.0ms

Steps

Iters	Range		Point
9	8.968674946987851e-17	1.9438689862588278e-11	1.9186871190009995e-11
8	-0.00013490814597532825	-1.2463973062393072e-08	-1.2659438482439053e-08

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample6.1s

Algorithm

intervals

Results

3.4s	3237×	body	1280	valid
980.0ms	635×	body	2560	valid
944.0ms	1841×	body	640	valid
255.0ms	801×	body	320	valid
97.0ms	1135×	body	80	valid
71.0ms	351×	body	160	valid