Details

sample210.0ms

Algorithm

intervals

Results

63.0ms	49×	body	1280	valid
59.0ms	31×	body	640	valid
36.0ms	140×	body	80	valid
18.0ms	26×	body	320	valid
5.0ms	10×	body	160	valid

simplify1.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	2093
5	2093
4	843
3	216
2	85
1	36
0	17

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* 2 J) (cos (/ K 2)))
9.4b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
7×	`associate-l`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 92

Calls

4 calls:

30.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
29.0ms	(* (cos (/ K 2)) (* -2 J))
32.0ms	(* (* 2 J) (cos (/ K 2)))
57.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
83.0ms	(* (cos (/ K 2)) (* -2 J))
82.0ms	(* (* 2 J) (cos (/ K 2)))
382.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	2090
3	2090
2	1564
1	413
0	161

prune656.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
9.5b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
9.5b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
27×	`add-cbrt-cube` `add-exp-log`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-l` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 89

Calls

4 calls:

75.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
149.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

391.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
365.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
280.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
255.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

simplify1.9s

Counts

101 → 101

Iterations

Iter	Nodes
done	2115
3	2115
2	940
1	270
0	114

prune653.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.5b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))) (* (cos (/ K 2)) (* -2 J)))))
9.5b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
9.5b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
9.5b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

rewrite371.0ms

Algorithm

rewrite-expression-head

Rules

27×	`pow1`
24×	`add-cbrt-cube` `add-exp-log`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `sqrt-prod`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`associate-r` `*-commutative`

Counts

4 → 81

Calls

4 calls:

357.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))) (* (cos (/ K 2)) (* -2 J)))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
1.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
10.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

series1.0s

Counts

4 → 12

Calls

4 calls:

326.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))) (* (sqrt (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))) (* (cos (/ K 2)) (* -2 J)))))
259.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
219.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
197.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

simplify1.8s

Counts

93 → 93

Iterations

Iter	Nodes
done	2009
3	2009
2	1136
1	305
0	116

prune598.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.5b

localize51.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (cos (/ K 2)))
0.2b	(cbrt (cos (/ K 2)))
0.2b	(cbrt (cos (/ K 2)))
9.4b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

33×	`pow1` `add-exp-log`
23×	`add-cbrt-cube`
22×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-l`
1×	`associate-r` `*-commutative`

Counts

4 → 78

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
216.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series800.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (cos (/ K 2)))
174.0ms	(cbrt (cos (/ K 2)))
147.0ms	(cbrt (cos (/ K 2)))
332.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify1.5s

Counts

90 → 90

Iterations

Iter	Nodes
done	2000
3	2000
2	1283
1	327
0	123

prune559.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 4.5b

regimes550.0ms

Accuracy

-14.1% (4.1b remaining)

Error of 7.6b against oracle of 3.5b and baseline of 7.1b

bsearch39.0ms

Steps

Iters	Range		Point
2	-1.4452110078089116e+239	-1.2809177034571467e+239	-1.424674344764941e+239

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample6.4s

Algorithm

intervals

Results

2.8s	1514×	body	1280	valid
1.4s	1278×	body	640	valid
1.2s	4305×	body	80	valid
522.0ms	628×	body	320	valid
134.0ms	278×	body	160	valid