Details

sample70.0ms

Algorithm

intervals

Results

18.0ms	40×	body	1280	valid
16.0ms	46×	body	640	valid
14.0ms	142×	body	80	valid
5.0ms	19×	body	320	valid
2.0ms	9×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize15.0ms

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)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
15×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`sqrt-prod`
7×	`unpow-prod-down`
4×	`sqrt-div` `pow-exp` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `sqr-pow`

Counts

4 → 85

Calls

4 calls:

7.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
55.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
25.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
131.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
184.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
138.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	453	1006
1	1965	898
2	5001	898

prune283.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.8b

localize19.0ms

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)
6.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
7.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log`
23×	`pow1`
21×	`add-cbrt-cube`
14×	`prod-exp`
11×	`*-un-lft-identity` `pow-prod-down` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
7×	`unpow-prod-down`
4×	`sqrt-div` `associate-r/` `associate-r*` `pow-exp` `sqrt-prod` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp`
2×	`flip3-+` `associate-l` `*-commutative` `flip-+`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv` `distribute-lft-out` `sqr-pow`

Counts

4 → 82

Calls

4 calls:

9.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
45.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
22.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series504.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
135.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
186.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
138.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	488	987
1	2021	866
2	5002	866

prune282.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 9.8b

localize20.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
7.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`sqrt-prod`
12×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`sqrt-div`
7×	`pow1` `cbrt-prod`
4×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `distribute-lft-out` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 65

Calls

4 calls:

12.0ms	(cbrt (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)))
22.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
26.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

220.0ms	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
137.0ms	(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)))
140.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	183	942
1	410	899
2	1386	895
3	5001	884

prune336.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (cos (/ K 2.0)))
0.4b	(cbrt (cos (/ K 2.0)))
6.4b	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.5b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite244.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

0.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
219.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
22.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (cos (/ K 2.0)))
144.0ms	(cbrt (cos (/ K 2.0)))
189.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
139.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	401	1337
1	1828	1008
2	5002	913

prune267.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 9.8b

regimes327.0ms

Accuracy

90.7% (0.5b remaining)

Error of 13.1b against oracle of 12.6b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	50
1	49	50

end0.0ms

sample2.0s

Algorithm

intervals

Results

732.0ms	1558×	body	1280	valid
443.0ms	4292×	body	80	valid
403.0ms	1181×	body	640	valid
168.0ms	651×	body	320	valid
59.0ms	322×	body	160	valid