Details

sample152.0ms

Algorithm

intervals

Results

67.0ms	295×	body	80	valid
36.0ms	34×	body	1280	valid
20.0ms	25×	body	640	valid
8.0ms	15×	body	320	valid
2.0ms	7×	body	160	valid

simplify2.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	2531
6	2531
5	1352
4	542
3	196
2	66
1	28
0	12

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* x (* sin cos)) (* x (* sin cos)))
0.3b	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
5.8b	(* x (* sin cos))
5.8b	(* x (* sin cos))

rewrite236.0ms

Algorithm

rewrite-expression-head

Rules

128×	`pow1`
97×	`add-cbrt-cube` `add-exp-log`
72×	`pow-prod-down`
60×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-plus` `associate-r` `-commutative` `associate-/l`
1×	`pow2` `clear-num` `associate-/r*` `frac-2neg` `div-sub` `swap-sqr` `cos-2` `div-inv`

Counts

4 → 146

Calls

4 calls:

91.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
95.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
30.0ms	(* x (* sin cos))
14.0ms	(* x (* sin cos))

series292.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(* (* x (* sin cos)) (* x (* sin cos)))
105.0ms	(/ (cos (* 2 x)) (* (* x (* sin cos)) (* x (* sin cos))))
50.0ms	(* x (* sin cos))
49.0ms	(* x (* sin cos))

simplify1.6s

Counts

158 → 158

Iterations

Iter	Nodes
done	2000
3	2000
2	1897
1	403
0	147

prune471.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.4b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
0.6b	(/ (cos (* 2 x)) (* x (* sin cos)))
5.8b	(* x (* sin cos))
5.8b	(* x (* sin cos))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-cbrt-cube` `add-exp-log`
30×	`prod-exp` `cbrt-unprod`
24×	`cbrt-undiv` `div-exp`
16×	`times-frac`
14×	`pow1`
12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
10×	`associate-/l*`
6×	`associate-l` `pow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`div-sub`
2×	`clear-num` `associate-/r` `frac-2neg` `associate-r` `-commutative` `cos-2`
1×	`associate-/l/`

Counts

4 → 123

Calls

4 calls:

52.0ms	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
22.0ms	(/ (cos (* 2 x)) (* x (* sin cos)))
21.0ms	(* x (* sin cos))
17.0ms	(* x (* sin cos))

series219.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (/ (cos (* 2 x)) (* x (* sin cos))) (* x (* sin cos)))
45.0ms	(/ (cos (* 2 x)) (* x (* sin cos)))
38.0ms	(* x (* sin cos))
31.0ms	(* x (* sin cos))

simplify997.0ms

Counts

135 → 135

Iterations

Iter	Nodes
done	2000
2	2000
1	441
0	165

prune588.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (cos (* 2 x)) x)
0.2b	(/ (/ (/ (cos (* 2 x)) x) (* sin cos)) (* x (* sin cos)))
5.8b	(* x (* sin cos))
6.1b	(/ (/ (cos (* 2 x)) x) (* sin cos))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

101×	`times-frac`
92×	`add-cbrt-cube` `add-exp-log`
43×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
40×	`cbrt-undiv` `div-exp`
33×	`associate-/l*`
26×	`prod-exp` `cbrt-unprod`
9×	`pow1` `div-inv`
6×	`div-sub`
5×	`associate-/r*`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down` `cos-2`
2×	`associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 182

Calls

4 calls:

15.0ms	(/ (cos (* 2 x)) x)
50.0ms	(/ (/ (/ (cos (* 2 x)) x) (* sin cos)) (* x (* sin cos)))
20.0ms	(* x (* sin cos))
30.0ms	(/ (/ (cos (* 2 x)) x) (* sin cos))

series241.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (cos (* 2 x)) x)
104.0ms	(/ (/ (/ (cos (* 2 x)) x) (* sin cos)) (* x (* sin cos)))
38.0ms	(* x (* sin cos))
55.0ms	(/ (/ (cos (* 2 x)) x) (* sin cos))

simplify1.1s

Counts

194 → 194

Iterations

Iter	Nodes
done	2001
2	2001
1	735
0	279

prune751.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (cos (* 2 x)))
0.2b	(/ (/ (/ 1 (/ x (cos (* 2 x)))) (* sin cos)) (* x (* sin cos)))
5.8b	(* x (* sin cos))
6.1b	(/ (/ 1 (/ x (cos (* 2 x)))) (* sin cos))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

453×	`times-frac`
284×	`add-exp-log`
158×	`div-exp`
155×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
140×	`add-cbrt-cube`
95×	`associate-/l*`
76×	`prod-exp`
70×	`cbrt-undiv`
36×	`cbrt-unprod`
21×	`div-inv`
16×	`rec-exp` `1-exp`
9×	`pow1`
5×	`associate-/r*`
4×	`expm1-log1p-u` `associate-/r/` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`clear-num` `frac-2neg` `associate-l` `pow-prod-down`
2×	`associate-/l/`
1×	`associate-r` `*-commutative`

Counts

4 → 351

Calls

4 calls:

9.0ms	(/ x (cos (* 2 x)))
53.0ms	(/ (/ (/ 1 (/ x (cos (* 2 x)))) (* sin cos)) (* x (* sin cos)))
18.0ms	(* x (* sin cos))
40.0ms	(/ (/ 1 (/ x (cos (* 2 x)))) (* sin cos))

series198.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ x (cos (* 2 x)))
80.0ms	(/ (/ (/ 1 (/ x (cos (* 2 x)))) (* sin cos)) (* x (* sin cos)))
42.0ms	(* x (* sin cos))
47.0ms	(/ (/ 1 (/ x (cos (* 2 x)))) (* sin cos))

simplify972.0ms

Counts

363 → 363

Iterations

Iter	Nodes
done	2011
2	2011
1	1620
0	577

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes181.0ms

Accuracy

-1.8% (2.8b remaining)

Error of 2.9b against oracle of 0.1b and baseline of 2.8b

bsearch280.0ms

Steps

Iters	Range		Point
10	1.4434334319750872e-170	5.6768435042774e-159	5.117094630849011e-162
8	-1.2710977012565344e+36	-1.2283864031141439e+33	-6.43178686487588e+34

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.8s	9100×	body	80	valid
1.1s	791×	body	1280	valid
843.0ms	1014×	body	640	valid
297.0ms	561×	body	320	valid
131.0ms	309×	body	160	valid