Details

sample80.0ms

Algorithm

intervals

Results

27.0ms	46×	body	1280	valid
17.0ms	44×	body	640	valid
12.0ms	131×	body	80	valid
5.0ms	19×	body	320	valid
3.0ms	16×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	13
1	75	13
2	139	13
3	207	13
4	375	13
5	1373	13
6	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize16.0ms

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)
6.7b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite256.0ms

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:

17.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
142.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
72.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
119.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
168.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
126.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	464	1076
1	1988	966
2	5001	965

prune562.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.9b

localize21.0ms

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

rewrite109.0ms

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:

17.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
17.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
20.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
52.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
40.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
44.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
445.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	489	993
1	2344	770
2	5001	770

prune535.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

localize25.0ms

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)))
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))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

18.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
17.0ms	(* (* -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))))
2.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series957.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
41.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
439.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
434.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	308	710
1	1231	636
2	5002	634

prune678.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.9b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
6.9b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.9b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.9b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log`
19×	`add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 69

Calls

4 calls:

69.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (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))))
1.0ms	(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))))

series2.1s

Counts

4 → 12

Calls

4 calls:

570.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (* (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))))
506.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
496.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
495.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify52.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	343	1759
1	1280	1423
2	5001	1367

prune969.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 6.9b

regimes376.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample2.3s

Algorithm

intervals

Results

899.0ms	1502×	body	1280	valid
517.0ms	1280×	body	640	valid
413.0ms	4292×	body	80	valid
178.0ms	626×	body	320	valid
63.0ms	303×	body	160	valid