Details

sample89.0ms

Algorithm

intervals

Results

29.0ms	49×	body	1280	valid
23.0ms	145×	body	80	valid
16.0ms	35×	body	640	valid
6.0ms	18×	body	320	valid
2.0ms	9×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize16.0ms

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)
8.3b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.2b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite107.0ms

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))))
30.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series512.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
136.0ms	(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))))
141.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (48.0ms)

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

prune347.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.6b

localize22.0ms

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)))
8.3b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite44.0ms

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)))
21.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series680.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
49.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
45.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
499.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify61.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (12.0ms)

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

prune330.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.1b	(/ 1 (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0)))))
8.3b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) (/ 2.0 2))))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

71×	`add-exp-log`
41×	`add-cbrt-cube`
37×	`prod-exp`
26×	`pow1`
19×	`cbrt-unprod`
13×	`add-sqr-sqrt` `associate-r` `pow-prod-down`
12×	`div-exp`
11×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-undiv` `rec-exp` `times-frac` `1-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-flip` `-commutative` `associate-/l`
2×	`div-inv`
1×	`frac-2neg` `associate-r/` `clear-num` `associate-/r` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 116

Calls

4 calls:

7.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
12.0ms	(/ 1 (* (* 2.0 J) (cos (/ K 2.0))))
34.0ms	(* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0)))))
22.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) (/ 2.0 2))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
65.0ms	(/ 1 (* (* 2.0 J) (cos (/ K 2.0))))
88.0ms	(* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0)))))
498.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) (/ 2.0 2))))

simplify73.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	601	1236
1	2868	966
2	5002	956

prune370.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.6b

localize26.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (* (* -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))))))
8.6b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.6b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.6b	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite33.0ms

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:

30.0ms	(* (* (* -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))))))
0.0ms	(cbrt (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))))

series2.4s

Counts

4 → 12

Calls

4 calls:

621.0ms	(* (* (* -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))))))
539.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
545.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
732.0ms	(cbrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (35.0ms)

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

prune359.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 8.6b

regimes270.0ms

Accuracy

0% (0.3b remaining)

Error of 8.4b against oracle of 8.1b and baseline of 8.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample2.6s

Algorithm

intervals

Results

923.0ms	1508×	body	1280	valid
596.0ms	4323×	body	80	valid
567.0ms	1246×	body	640	valid
206.0ms	613×	body	320	valid
72.0ms	313×	body	160	valid