Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	54×	body	1280	valid
13.0ms	50×	body	640	valid
9.0ms	129×	body	80	valid
3.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify46.0ms

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: 16.9b

localize18.0ms

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)
7.8b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite258.0ms

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:

19.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
149.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
66.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series481.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
123.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
179.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
133.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (11.0ms)

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

prune304.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.4b

localize18.0ms

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)
7.8b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.0b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite233.0ms

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:

18.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
22.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
125.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
64.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series474.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
127.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
172.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
135.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

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

prune286.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 12.4b

localize22.0ms

Local error

Found 4 expressions with local error:

7.8b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.8b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.0b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.0b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite254.0ms

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:

63.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
63.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
62.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
64.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
206.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
135.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
134.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify57.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (46.0ms)

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

prune372.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 12.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
7.8b	(* (* (* (* -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))))
8.0b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite540.0ms

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:

1.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
471.0ms	(* (* (* (* -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))))
65.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series610.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (cos (/ K 2.0)))
149.0ms	(cbrt (cos (/ K 2.0)))
182.0ms	(* (* (* (* -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))))
132.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	401	1338
1	1828	1008
2	5002	913

prune277.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 12.4b

regimes417.0ms

Accuracy

88.7% (0.6b remaining)

Error of 13.5b against oracle of 12.9b and baseline of 18.5b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	50
1	49	50

end0.0ms

sample1.7s

Algorithm

intervals

Results

560.0ms	1463×	body	1280	valid
346.0ms	1289×	body	640	valid
311.0ms	4321×	body	80	valid
126.0ms	617×	body	320	valid
43.0ms	313×	body	160	valid