Details

sample122.0ms

Algorithm

intervals

Results

38.0ms	48×	body	1280	valid
26.0ms	46×	body	640	valid
18.0ms	128×	body	80	valid
11.0ms	26×	body	320	valid
2.0ms	8×	body	160	valid

simplify2.9s

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: 17.9b

localize51.0ms

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)
6.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite269.0ms

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:

14.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
17.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
127.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
108.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series719.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
228.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
233.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
196.0ms	(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

prune740.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize46.0ms

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)))
6.6b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite128.0ms

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:

18.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
14.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
21.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
70.0ms	(* (* (* -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:

122.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
91.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
85.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
717.0ms	(* (* (* -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

100 → 100

Iterations

Iter	Nodes
done	5000
2	3021
1	499
0	194

prune935.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.9b

localize55.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
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)))
6.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
7.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
11.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
25.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

613.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
615.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
136.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
771.0ms	(* (* -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

116 → 116

Iterations

Iter	Nodes
done	5000
2	3108
1	639
0	258

prune901.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

localize94.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
0.2b	(* (* (* (* 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)))))
6.7b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.7b	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

rewrite249.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

23.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
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)))))
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))))

series2.9s

Counts

4 → 12

Calls

4 calls:

525.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
877.0ms	(* (* (* (* 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)))))
775.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
734.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

simplify1.5s

Counts

121 → 121

Iterations

Iter	Nodes
done	5000
2	3387
1	675
0	274

prune1.2s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.9b

regimes732.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.5s	1509×	body	1280	valid
1.1s	4309×	body	80	valid
855.0ms	1244×	body	640	valid
229.0ms	618×	body	320	valid
81.0ms	325×	body	160	valid