Details

sample118.0ms

Algorithm

intervals

Results

38.0ms	50×	body	640	valid
35.0ms	45×	body	1280	valid
19.0ms	136×	body	80	valid
6.0ms	12×	body	320	valid
4.0ms	13×	body	160	valid

simplify967.0ms

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.2b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* 2 J) (cos (/ K 2)))
0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
7.2b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

rewrite97.0ms

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:

19.0ms	(* (cos (/ K 2)) (* -2 J))
17.0ms	(* (* 2 J) (cos (/ K 2)))
18.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
41.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(* (cos (/ K 2)) (* -2 J))
53.0ms	(* (* 2 J) (cos (/ K 2)))
93.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
282.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (cos (/ K 2)) (* -2 J)))

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	2057
3	2057
2	1560
1	416
0	161

prune566.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2)))
0.1b	(* (* 2 J) (cos (/ K 2)))
0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
7.2b	(* (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-cbrt-cube` `add-exp-log`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r`
5×	`associate-l`
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` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

14.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2)))
28.0ms	(* (* 2 J) (cos (/ K 2)))
26.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
48.0ms	(* (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

series821.0ms

Counts

4 → 12

Calls

4 calls:

271.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2)))
68.0ms	(* (* 2 J) (cos (/ K 2)))
137.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
344.0ms	(* (* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (cos (/ K 2))) (* -2 J))

simplify1.3s

Counts

105 → 105

Iterations

Iter	Nodes
done	2016
3	2016
2	1589
1	404
0	159

prune637.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
0.1b	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
7.2b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
7.2b	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

rewrite198.0ms

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:

41.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
151.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
2.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
2.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

324.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J)))
352.0ms	(* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2)))))) (* (cos (/ K 2)) (* -2 J))))
277.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))
252.0ms	(sqrt (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))))

simplify1.5s

Counts

101 → 101

Iterations

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

prune539.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 3.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2 J) (cos (/ K 2)))
0.1b	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
0.1b	(/ U (* (* 2 J) (cos (/ K 2))))
6.2b	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

rewrite223.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-cbrt-cube` `add-exp-log`
32×	`pow1`
22×	`prod-exp` `cbrt-unprod`
19×	`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 → 101

Calls

4 calls:

20.0ms	(* (* 2 J) (cos (/ K 2)))
64.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
16.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
119.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

series597.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (* 2 J) (cos (/ K 2)))
84.0ms	(* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J)))
120.0ms	(/ U (* (* 2 J) (cos (/ K 2))))
333.0ms	(* (hypot 1 (/ U (* (* 2 J) (cos (/ K 2))))) (* (sqrt (cos (/ K 2))) (* (sqrt (cos (/ K 2))) (* -2 J))))

simplify1.6s

Counts

113 → 113

Iterations

Iter	Nodes
done	2006
3	2006
2	1866
1	476
0	179

prune595.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.1b

regimes455.0ms

Accuracy

-17.7% (4.6b remaining)

Error of 8.5b against oracle of 3.8b and baseline of 7.8b

bsearch351.0ms

Steps

Iters	Range		Point
9	7.747027600400188e-210	8.221580356149798e-204	7.865937310037316e-210
8	-1.2318312220751903e-280	-9.004630353795933e-284	-4.840558415743229e-282

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample6.3s

Algorithm

intervals

Results

2.4s	1464×	body	1280	valid
1.6s	4326×	body	80	valid
1.3s	1252×	body	640	valid
545.0ms	624×	body	320	valid
210.0ms	337×	body	160	valid