Details

sample153.0ms

Algorithm

intervals

Results

46.0ms	49×	body	1280	valid
24.0ms	37×	body	640	valid
23.0ms	137×	body	80	valid
12.0ms	25×	body	320	valid
3.0ms	8×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
done	5038
5	4827
4	843
3	216
2	85
1	36
0	17

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.9b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2 (cos (/ K 2))) J))
0.1b	(* (cos (/ K 2)) (* -2 J))
0.1b	(* (* 2 (cos (/ K 2))) J)
7.9b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (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:

20.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
14.0ms	(* (cos (/ K 2)) (* -2 J))
22.0ms	(* (* 2 (cos (/ K 2))) J)
39.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

series572.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
69.0ms	(* (cos (/ K 2)) (* -2 J))
69.0ms	(* (* 2 (cos (/ K 2))) J)
340.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

simplify2.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1590
1	418
0	164

prune534.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
0.1b	(/ U (* (* 2 (cos (/ K 2))) J))
0.1b	(* (* 2 (cos (/ K 2))) J)
7.9b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

rewrite82.0ms

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:

7.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
22.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
18.0ms	(* (* 2 (cos (/ K 2))) J)
33.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

series734.0ms

Counts

4 → 12

Calls

4 calls:

258.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2)))
92.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
69.0ms	(* (* 2 (cos (/ K 2))) J)
315.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (cos (/ K 2))) (* -2 J))

simplify1.7s

Counts

105 → 105

Iterations

Iter	Nodes
done	5002
2	1593
1	419
0	165

prune639.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.0b

localize56.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

143.0ms	(* (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.4s

Counts

4 → 12

Calls

4 calls:

344.0ms	(* (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))) (* (cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J)))) (* (cos (/ K 2)) (* -2 J))))
312.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
390.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
386.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify3.9s

Counts

91 → 91

Iterations

Iter	Nodes
done	5005
3	4933
2	1107
1	309
0	124

prune656.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.0b

localize109.0ms

Local error

Found 4 expressions with local error:

8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.1b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

1.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
1.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
2.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

series1.4s

Counts

4 → 12

Calls

4 calls:

336.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
348.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
371.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
337.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

simplify2.0s

Counts

68 → 68

Iterations

Iter	Nodes
done	5012
4	1981
3	528
2	185
1	87
0	49

prune554.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 5.0b

regimes540.0ms

Accuracy

-9.1% (4.4b remaining)

Error of 8.2b against oracle of 3.8b and baseline of 7.9b

bsearch110.0ms

Steps

Iters	Range		Point
5	-8.091786763451962e+243	-4.0158444704749664e+243	-6.5450850664377556e+243

simplify6.0ms

Iterations

Iter	Nodes
done	26
1	26
0	19

end0.0ms

sample6.5s

Algorithm

intervals

Results

2.1s	1477×	body	1280	valid
1.9s	1252×	body	640	valid
1.2s	4333×	body	80	valid
948.0ms	629×	body	320	valid
140.0ms	310×	body	160	valid