Details

sample54.0ms

Algorithm

intervals

Results

18.0ms	49×	body	1280	valid
10.0ms	150×	body	80	valid
8.0ms	30×	body	640	valid
4.0ms	24×	body	320	valid
1.0ms	4×	body	160	valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	128	24
4	172	24
5	279	24
6	662	24
7	2082	24
done	5001	24

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.3b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 96

Calls

4 calls:

7.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
59.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
27.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
131.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
189.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
144.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify724.0ms

Counts

108 → 108

Iterations

Useful iterations: 2 (210.0ms)

Iter	Nodes	Cost
0	201	2139
1	466	1925
2	1555	1736
done	5000	1736

prune334.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

7.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
7.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
7.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series674.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
48.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
46.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
494.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify753.0ms

Counts

100 → 100

Iterations

Useful iterations: 2 (243.0ms)

Iter	Nodes	Cost
0	193	1843
1	489	1816
2	2002	1415
done	5001	1415

prune323.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
0.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
6.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

84.0ms	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
23.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
1.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.0s

Counts

4 → 12

Calls

4 calls:

492.0ms	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
532.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
474.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
490.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify710.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (167.0ms)

Iter	Nodes	Cost
0	156	3825
1	401	3009
2	1500	2451
done	5000	2451

prune365.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.6b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (* (* -2.0 J) (cos (/ K 2.0))))
6.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.7b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.7b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative`

Counts

4 → 64

Calls

4 calls:

18.0ms	(* (fabs (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (* (* -2.0 J) (cos (/ K 2.0))))
1.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
0.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.7s

Counts

4 → 12

Calls

4 calls:

111.0ms	(* (fabs (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (* (* -2.0 J) (cos (/ K 2.0))))
504.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
551.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
549.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.4s

Counts

76 → 76

Iterations

Useful iterations: 3 (406.0ms)

Iter	Nodes	Cost
0	148	2240
1	335	2175
2	992	1818
3	3856	1812
done	5001	1812

prune386.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 6.6b

regimes252.0ms

Accuracy

0% (0.3b remaining)

Error of 8.0b against oracle of 7.8b and baseline of 8.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	26
1	24	26
done	24	26

end0.0ms

sample1.5s

Algorithm

intervals

Results

551.0ms	1482×	body	1280	valid
312.0ms	1195×	body	640	valid
306.0ms	4343×	body	80	valid
122.0ms	663×	body	320	valid
42.0ms	322×	body	160	valid