Details

sample141.0ms

Algorithm

intervals

Results

80.0ms	149×	body	1280	valid
26.0ms	23×	body	2560	valid
16.0ms	51×	body	640	valid
5.0ms	22×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify3.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize19.0ms

Local error

Found 2 expressions with local error:

0.9b	(- (cos (+ eps x)) (cos x))
3.4b	(cos (+ eps x))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

12.0ms	(- (cos (+ eps x)) (cos x))
13.0ms	(cos (+ eps x))

series120.0ms

Counts

2 → 6

Calls

2 calls:

73.0ms	(- (cos (+ eps x)) (cos x))
47.0ms	(cos (+ eps x))

simplify769.0ms

Counts

46 → 46

Iterations

Iter	Nodes
done	5001
2	671
1	193
0	91

prune220.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
0.2b	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 51

Calls

3 calls:

31.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
30.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
6.0ms	(sin (/ (fma 2 x eps) 2))

series230.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* -2 (* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2))))
87.0ms	(* (sin (/ eps 2)) (sin (/ (fma 2 x eps) 2)))
44.0ms	(sin (/ (fma 2 x eps) 2))

simplify593.0ms

Counts

60 → 60

Iterations

Iter	Nodes
done	5000
2	802
1	221
0	99

prune425.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.5b	(sin (/ (fma 2 x eps) 2))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-cbrt-cube` `add-exp-log`
3×	`add-sqr-sqrt` `-un-lft-identity` `associate-r*` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`associate-l` `*-commutative`

Counts

2 → 29

Calls

2 calls:

24.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series138.0ms

Counts

2 → 6

Calls

2 calls:

93.0ms	(* (* -2 (sin (/ eps 2))) (sin (/ (fma 2 x eps) 2)))
45.0ms	(sin (/ (fma 2 x eps) 2))

simplify1.1s

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
2	815
1	171
0	71

prune283.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (sin (/ (fma x 2 eps) 2)))
0.2b	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma x 2 eps) 2)))))
0.3b	(log1p (expm1 (sin (/ (fma x 2 eps) 2))))
3.5b	(sin (/ (fma x 2 eps) 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

9×	`pow1` `add-cbrt-cube` `add-exp-log`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u`
4×	`expm1-log1p-u` `add-log-exp`
3×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `associate-l` `log1p-expm1` `*-commutative` `expm1-udef`

Counts

4 → 51

Calls

4 calls:

0.0ms	(expm1 (sin (/ (fma x 2 eps) 2)))
30.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma x 2 eps) 2)))))
0.0ms	(log1p (expm1 (sin (/ (fma x 2 eps) 2))))
3.0ms	(sin (/ (fma x 2 eps) 2))

series343.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(expm1 (sin (/ (fma x 2 eps) 2)))
158.0ms	(* (* -2 (sin (/ eps 2))) (log1p (expm1 (sin (/ (fma x 2 eps) 2)))))
77.0ms	(log1p (expm1 (sin (/ (fma x 2 eps) 2))))
40.0ms	(sin (/ (fma x 2 eps) 2))

simplify653.0ms

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
2	962
1	220
0	96

prune380.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.3b

regimes276.0ms

Accuracy

96.5% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 15.2b

bsearch201.0ms

Steps

Iters	Range		Point
10	257785.57693934403	2.1403836343929554e+18	260530.5202352258
11	-496427297.3881253	-4.632829109756021e-12	-8.608808965388138e-05

simplify3.0ms

Iterations

Iter	Nodes
done	32
1	32
0	25

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.1s	4372×	body	1280	valid
964.0ms	622×	body	2560	valid
885.0ms	1910×	body	640	valid
193.0ms	733×	body	320	valid
59.0ms	290×	body	160	valid
7.0ms	73×	body	80	valid