Details

sample98.0ms

Algorithm

intervals

Results

27.0ms	39×	body	1280	valid
24.0ms	48×	body	640	valid
18.0ms	139×	body	80	valid
8.0ms	22×	body	320	valid
2.0ms	8×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

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

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.6b

localize52.0ms

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)
8.5b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

rewrite131.0ms

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 (cos (/ K 2))) J))
21.0ms	(* (cos (/ K 2)) (* -2 J))
20.0ms	(* (* 2 (cos (/ K 2))) J)
66.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

series598.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ U (* (* 2 (cos (/ K 2))) J))
82.0ms	(* (cos (/ K 2)) (* -2 J))
68.0ms	(* (* 2 (cos (/ K 2))) J)
362.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cos (/ K 2)) (* -2 J)))

simplify1.7s

Counts

104 → 104

Iterations

Iter	Nodes
done	5001
2	1590
1	418
0	164

prune632.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize50.0ms

Local error

Found 4 expressions with local error:

1.3b	(* (* (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))))
8.9b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.9b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
8.9b	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))

rewrite219.0ms

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:

213.0ms	(* (* (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))))

series1.5s

Counts

4 → 12

Calls

4 calls:

332.0ms	(* (* (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))))
346.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
406.0ms	(cbrt (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))))
375.0ms	(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

prune516.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize57.0ms

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)))
8.5b	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

rewrite241.0ms

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)))
235.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

series812.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(cbrt (cos (/ K 2)))
149.0ms	(cbrt (cos (/ K 2)))
145.0ms	(cbrt (cos (/ K 2)))
350.0ms	(* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2)))) (* (cbrt (cos (/ K 2))) (* -2 J))))

simplify2.2s

Counts

90 → 90

Iterations

Iter	Nodes
done	5001
2	1288
1	329
0	124

prune546.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize40.0ms

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)))
8.6b	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (* -2 J)))

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

40×	`pow1` `add-exp-log`
28×	`add-cbrt-cube`
27×	`pow-prod-down` `prod-exp` `cbrt-unprod`
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 → 82

Calls

4 calls:

1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
1.0ms	(cbrt (cos (/ K 2)))
122.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (* -2 J)))

series704.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (cos (/ K 2)))
109.0ms	(cbrt (cos (/ K 2)))
116.0ms	(cbrt (cos (/ K 2)))
315.0ms	(* (* (hypot 1 (/ U (* (* 2 (cos (/ K 2))) J))) (* (cbrt (cos (/ K 2))) (cbrt (cos (/ K 2))))) (* (cbrt (cos (/ K 2))) (* -2 J)))

simplify2.0s

Counts

94 → 94

Iterations

Iter	Nodes
done	5000
2	1216
1	304
0	117

prune399.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

regimes487.0ms

Accuracy

-17.2% (4.0b remaining)

Error of 7.9b against oracle of 4.0b and baseline of 7.3b

bsearch249.0ms

Steps

Iters	Range		Point
6	-1.6928568579103404e-223	-1.5066516687482977e-224	-4.963799731811966e-224
10	-6.480897382713564e-175	-1.0297009910709892e-187	-1.0416216881156113e-187

simplify8.0ms

Iterations

Iter	Nodes
done	32
1	32
0	22

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	1417×	body	1280	valid
1.2s	1186×	body	640	valid
1.1s	4462×	body	80	valid
274.0ms	597×	body	320	valid
124.0ms	339×	body	160	valid