Details

sample96.0ms

Algorithm

intervals

Results

34.0ms	53×	body	1280	valid
18.0ms	38×	body	640	valid
17.0ms	135×	body	80	valid
8.0ms	21×	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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

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)
7.1b	(* (* (* -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)))

rewrite101.0ms

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)))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
60.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
35.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
50.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
38.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 1 (13.0ms)

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

prune855.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 12.7b

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)
7.1b	(* (* -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)))

rewrite91.0ms

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:

7.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
9.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
49.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (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)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
35.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
50.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
39.0ms	(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

prune824.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 12.7b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
1.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
15.0b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
15.0b	(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)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
42.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
69.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
68.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify43.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

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

prune1.2s

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 12.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
7.1b	(* (* (* (* -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))))
9.2b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite253.0ms

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)))
226.0ms	(* (* (* (* -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))))
23.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series120.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt (cos (/ K 2.0)))
15.0ms	(cbrt (cos (/ K 2.0)))
52.0ms	(* (* (* (* -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))))
39.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (55.0ms)

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

prune801.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 12.6b

regimes1.1s

Accuracy

90.7% (0.5b remaining)

Error of 12.9b against oracle of 12.4b and baseline of 17.9b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.0s	1555×	body	1280	valid
608.0ms	1245×	body	640	valid
533.0ms	4237×	body	80	valid
232.0ms	641×	body	320	valid
79.0ms	324×	body	160	valid