Details

sample176.0ms

Algorithm

intervals

Results

58.0ms	51×	body	1280	valid
43.0ms	135×	body	80	valid
38.0ms	41×	body	640	valid
10.0ms	16×	body	320	valid
6.0ms	13×	body	160	valid

simplify868.0ms

Counts

1 → 1

Iterations

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

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.3b

localize30.0ms

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)))
8.3b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite124.0ms

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:

22.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
24.0ms	(* (cos (/ K 2)) (* -2 J))
28.0ms	(* (* 2 J) (cos (/ K 2)))
48.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series593.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
75.0ms	(* (cos (/ K 2)) (* -2 J))
74.0ms	(* (* 2 J) (cos (/ K 2)))
321.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.2s

Counts

104 → 104

Iterations

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

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.5b

localize48.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
0.3b	(cbrt (cos (/ K 2)))
8.3b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite221.0ms

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)))
217.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series692.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(cbrt (cos (/ K 2)))
137.0ms	(cbrt (cos (/ K 2)))
115.0ms	(cbrt (cos (/ K 2)))
312.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify1.3s

Counts

90 → 90

Iterations

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

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.5b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (* (cos (/ K 2)) (* -2 J)))
0.5b	(cbrt (* (cos (/ K 2)) (* -2 J)))
0.5b	(cbrt (* (cos (/ K 2)) (* -2 J)))
8.3b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (* (cos (/ K 2)) (* -2 J))) (cbrt (* (cos (/ K 2)) (* -2 J)))) (cbrt (* (cos (/ K 2)) (* -2 J)))))

rewrite245.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

9.0ms	(cbrt (* (cos (/ K 2)) (* -2 J)))
9.0ms	(cbrt (* (cos (/ K 2)) (* -2 J)))
15.0ms	(cbrt (* (cos (/ K 2)) (* -2 J)))
210.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (* (cos (/ K 2)) (* -2 J))) (cbrt (* (cos (/ K 2)) (* -2 J)))) (cbrt (* (cos (/ K 2)) (* -2 J)))))

series904.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt (* (cos (/ K 2)) (* -2 J)))
153.0ms	(cbrt (* (cos (/ K 2)) (* -2 J)))
142.0ms	(cbrt (* (cos (/ K 2)) (* -2 J)))
433.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (* (cbrt (* (cos (/ K 2)) (* -2 J))) (cbrt (* (cos (/ K 2)) (* -2 J)))) (cbrt (* (cos (/ K 2)) (* -2 J)))))

simplify1.4s

Counts

72 → 72

Iterations

Iter	Nodes
done	2002
3	2002
2	674
1	231
0	99

prune1.1s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (cos (/ K 2))) (* -2 J))
0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
0.1b	(* (* 2 J) (cos (/ K 2)))
6.6b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-cbrt-cube` `add-exp-log`
28×	`pow1`
19×	`prod-exp` `cbrt-unprod`
16×	`pow-prod-down`
10×	`add-sqr-sqrt` `-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `-commutative` `sqrt-prod` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 98

Calls

4 calls:

32.0ms	(* (sqrt (cos (/ K 2))) (* -2 J))
32.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
32.0ms	(* (* 2 J) (cos (/ K 2)))
154.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

series642.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(* (sqrt (cos (/ K 2))) (* -2 J))
131.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
79.0ms	(* (* 2 J) (cos (/ K 2)))
346.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	2000
3	2000
2	1888
1	486
0	183

prune1.6s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.5b

regimes413.0ms

Accuracy

4.3% (4.1b remaining)

Error of 8.0b against oracle of 3.9b and baseline of 8.1b

bsearch139.0ms

Steps

Iters	Range		Point
7	-1.2833237315415606e-307	1.660299618472118e-308	-1.2687631742535287e-307
2	-5.1834993257123745e-282	-4.694982565212425e-282	-5.000305540524894e-282

simplify4.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample6.3s

Algorithm

intervals

Results

3.0s	1481×	body	1280	valid
1.4s	1280×	body	640	valid
1.1s	4310×	body	80	valid
491.0ms	605×	body	320	valid
149.0ms	328×	body	160	valid