Details

sample53.0ms

Algorithm

intervals

Results

17.0ms	47×	body	1280	valid
9.0ms	141×	body	80	valid
9.0ms	35×	body	640	valid
4.0ms	19×	body	320	valid
2.0ms	14×	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: 18.4b

localize15.0ms

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)
8.0b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite100.0ms

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))))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
54.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

series544.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
134.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
185.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	543	1086
1	2465	960
2	5001	960

prune311.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 13.2b

localize19.0ms

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)
8.0b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

7.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
48.0ms	(* (* -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)))

series560.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
139.0ms	(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)))))
141.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	537	1066
1	2238	928
2	5001	928

prune291.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 13.2b

localize18.0ms

Local error

Found 4 expressions with local error:

8.1b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.1b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite98.0ms

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:

25.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
23.0ms	(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)))
25.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series729.0ms

Counts

4 → 12

Calls

4 calls:

219.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
218.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
146.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
145.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify61.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (45.0ms)

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

prune339.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 13.2b

localize27.0ms

Local error

Found 4 expressions with local error:

8.3b	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
9.1b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite83.0ms

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

series657.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(cbrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
150.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
150.0ms	(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)))

simplify52.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (41.0ms)

Iter	Nodes	Cost
0	183	939
1	410	899
2	1386	895
3	5001	884

prune376.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 13.2b

regimes284.0ms

Accuracy

90.9% (0.5b remaining)

Error of 13.0b against oracle of 12.5b and baseline of 18.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	50
1	45	50

end0.0ms

sample1.6s

Algorithm

intervals

Results

543.0ms	1467×	body	1280	valid
348.0ms	1348×	body	640	valid
295.0ms	4230×	body	80	valid
117.0ms	613×	body	320	valid
48.0ms	344×	body	160	valid