Details

sample117.0ms

Algorithm

intervals

Results

36.0ms	51×	body	1280	valid
23.0ms	47×	body	640	valid
17.0ms	127×	body	80	valid
10.0ms	22×	body	320	valid
3.0ms	9×	body	160	valid

simplify2.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3226
5	495
4	209
3	135
2	72
1	34
0	17

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 18.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.1b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.9b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite274.0ms

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-l` `associate-r/` `-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:

15.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
25.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
156.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
76.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series788.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
194.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
305.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
230.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify1.4s

Counts

108 → 108

Iterations

Iter	Nodes
done	5000
2	2432
1	519
0	200

prune864.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.4b

localize52.0ms

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)))
7.1b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite146.0ms

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` `associate-r*` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `-commutative` `associate-/l`
1×	`clear-num` `associate-/r*` `frac-2neg` `div-inv`

Counts

4 → 88

Calls

4 calls:

19.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
23.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
15.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
87.0ms	(* (* (* -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:

124.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
90.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
63.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
742.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify1.5s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	3021
1	499
0	194

prune791.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.4b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b

(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

0.1b

(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))

7.1b

(* (* -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

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

Counts

3 → 94

Calls

3 calls:

6.0ms

(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

12.0ms

(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))

24.0ms

(* (* -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

3 → 9

Calls

3 calls:

698.0ms

(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

130.0ms

(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))

758.0ms

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

simplify2.4s

Counts

103 → 103

Iterations

Iter	Nodes
done	5001
2	3075
1	613
0	245

prune752.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 7.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (* J -2.0) (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)))))
0.1b	(* (* (* J -2.0) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
7.1b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
7.1b	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

rewrite314.0ms

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-r` `sqrt-prod`
10×	`*-un-lft-identity` `add-cube-cbrt`
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:

218.0ms	(* (* (* (* J -2.0) (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)))))
89.0ms	(* (* (* J -2.0) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
2.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
2.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

series3.2s

Counts

4 → 12

Calls

4 calls:

917.0ms	(* (* (* (* J -2.0) (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)))))
789.0ms	(* (* (* J -2.0) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))
767.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
693.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	2336
1	454
0	183

prune749.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 7.4b

regimes745.0ms

Accuracy

0% (0.3b remaining)

Error of 7.8b against oracle of 7.5b and baseline of 7.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.5s	1469×	body	1280	valid
1.1s	1311×	body	640	valid
784.0ms	4324×	body	80	valid
221.0ms	602×	body	320	valid
80.0ms	296×	body	160	valid