Details

sample67.0ms

Algorithm

intervals

Results

19.0ms	45×	body	1280	valid
16.0ms	147×	body	80	valid
11.0ms	34×	body	640	valid
3.0ms	14×	body	320	valid
3.0ms	17×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	13
1	74	13
2	138	13
3	203	13
4	368	13
5	1361	13
6	5001	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
7.7b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.8b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`*-un-lft-identity`
15×	`pow1`
13×	`add-sqr-sqrt`
12×	`add-cube-cbrt` `prod-exp`
9×	`cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down` `associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `clear-num` `associate-/r` `-commutative` `sqr-pow`

Counts

4 → 90

Calls

4 calls:

7.0ms	(/ U (* (* 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))))
24.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series564.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
138.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
191.0ms	(* (* (* -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)))

simplify67.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	543	1085
1	2466	960
2	5002	960

prune317.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)
0.2b	(* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0)))))
7.7b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0))))
8.8b	(sqrt (+ 1.0 (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
44×	`prod-exp`
27×	`add-cbrt-cube`
19×	`pow1`
15×	`*-un-lft-identity`
14×	`add-sqr-sqrt` `associate-r`
13×	`cbrt-unprod`
12×	`div-exp`
11×	`add-cube-cbrt` `pow-exp`
8×	`pow-prod-down` `sqrt-prod`
6×	`rec-exp` `1-exp`
4×	`sqrt-div` `associate-l` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `times-frac` `associate-*r/`
2×	`pow-pow` `flip3-+` `*-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `unpow-prod-down` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `un-div-inv` `div-inv` `unswap-sqr` `sqr-pow`

Counts

4 → 105

Calls

4 calls:

31.0ms	(pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)
36.0ms	(* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0)))))
30.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0))))
5.0ms	(sqrt (+ 1.0 (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)))

series563.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)
90.0ms	(* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0)))))
193.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0))))
147.0ms	(sqrt (+ 1.0 (pow (* U (/ 1 (* (* 2.0 J) (cos (/ K 2.0))))) 2.0)))

simplify78.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	627	1244
1	2974	1062
2	5001	1057

prune296.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 12.2b

localize26.0ms

Local error

Found 4 expressions with local error:

7.6b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.6b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.8b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.8b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

32×	`sqrt-prod`
18×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
12×	`sqrt-div`
10×	`pow1` `add-cube-cbrt` `sqrt-pow1`
6×	`rem-sqrt-square` `pow1/2`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`

Counts

4 → 76

Calls

4 calls:

24.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
26.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

222.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
221.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
147.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
143.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	189	1016
1	461	986
2	1696	986
3	5001	962

prune353.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 12.2b

localize23.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.3b	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
14.5b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
14.5b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1`
16×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
13×	`cbrt-prod`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`sqrt-prod`
6×	`cbrt-div`
4×	`add-log-exp`
3×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div`
1×	`pow1/2` `associate-r` `associate-l` `*-commutative`

Counts

4 → 71

Calls

4 calls:

26.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
10.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
12.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series761.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
82.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
226.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
226.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify52.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	347	1291
1	1206	1104
2	5001	1096

prune358.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.2b

regimes327.0ms

Accuracy

92.4% (0.4b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 18.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	51
1	57	51

end0.0ms

sample2.0s

Algorithm

intervals

Results

663.0ms	1515×	body	1280	valid
495.0ms	4234×	body	80	valid
397.0ms	1278×	body	640	valid
158.0ms	633×	body	320	valid
60.0ms	345×	body	160	valid