Details

sample73.0ms

Algorithm

intervals

Results

20.0ms	45×	body	1280	valid
15.0ms	45×	body	640	valid
11.0ms	123×	body	80	valid
7.0ms	30×	body	320	valid
2.0ms	13×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	24
1	34	24
2	72	24
3	133	24
4	194	24
5	315	24
6	754	24
7	2539	24
done	5001	24

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite418.0ms

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:

45.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
26.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
197.0ms	(* (* (* -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)))

series703.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
200.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
239.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
202.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.5s

Counts

108 → 108

Iterations

Useful iterations: 2 (386.0ms)

Iter	Nodes	Cost
0	201	2139
1	452	1925
2	1479	1736
done	5001	1736

prune527.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(* (* 2.0 J) (cos (/ K 2.0)))
0.2b	(* (* -2.0 J) (cos (/ K 2.0)))
7.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite173.0ms

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:

37.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
33.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
20.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
78.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series1.0s

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
63.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
53.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
733.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.6s

Counts

100 → 100

Iterations

Useful iterations: 2 (370.0ms)

Iter	Nodes	Cost
0	193	1843
1	478	1816
2	1899	1415
done	5000	1415

prune523.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.7b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (cos (/ K 2.0)) (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)))
7.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

24.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
11.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
19.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
42.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series1.6s

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
613.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
63.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
755.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify1.4s

Counts

101 → 101

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	206	2273
1	509	2248
2	1956	1753
done	5000	1752

prune484.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* -2.0 J) (cos (/ K 2.0)))
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))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
7.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
7.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite379.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

38.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
333.0ms	(* (* (* (* -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)))))
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))))

series2.3s

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
752.0ms	(* (* (* (* -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)))))
755.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
690.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.8s

Counts

91 → 91

Iterations

Useful iterations: 2 (278.0ms)

Iter	Nodes	Cost
0	152	3025
1	370	2316
2	1400	1857
done	5001	1857

prune532.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 7.6b

regimes532.0ms

Accuracy

0% (0.3b remaining)

Error of 7.9b against oracle of 7.7b and baseline of 7.9b

bsearch0.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.2s	1517×	body	1280	valid
1.2s	1196×	body	640	valid
756.0ms	4369×	body	80	valid
751.0ms	604×	body	320	valid
83.0ms	316×	body	160	valid