Details

sample48.0ms

Algorithm

intervals

Results

17.0ms	255×	body	80	valid
12.0ms	237×	body	80	overflowed
0.0ms	1×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	34	13
1	75	13
2	139	13
3	207	13
4	375	13
5	1373	13
6	5001	13

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* -2.0 J) (cos (/ K 2.0)))
0.2b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.4b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-exp-log`
20×	`pow1`
18×	`add-cbrt-cube`
17×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
12×	`prod-exp`
11×	`add-cube-cbrt`
10×	`associate-r`
9×	`pow-prod-down` `cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `times-frac` `div-exp` `hypot-def`
2×	`flip3-+` `associate-r/` `associate-l` `-commutative` `flip-+` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 96

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)
62.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
27.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series550.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
138.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
202.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
156.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	464	1076
1	1988	966
2	5001	965

prune345.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.0b	(* (* 2.0 J) (cos (/ K 2.0)))
0.0b	(* (* -2.0 J) (cos (/ K 2.0)))
8.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log` `add-cbrt-cube`
23×	`pow1`
15×	`prod-exp` `cbrt-unprod`
12×	`pow-prod-down`
9×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `times-frac` `div-exp` `associate-l` `-commutative` `associate-/l`
1×	`frac-2neg` `clear-num` `associate-/r*` `div-inv`

Counts

4 → 88

Calls

4 calls:

7.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
7.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
7.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
23.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
53.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
49.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
532.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify63.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	489	993
1	2344	770
2	5001	770

prune334.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (cos (/ K 2.0)))
0.1b	(cbrt (cos (/ K 2.0)))
0.1b	(cbrt (cos (/ K 2.0)))
8.4b	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite200.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r`
1×	`associate-l` `*-commutative`

Counts

4 → 71

Calls

4 calls:

0.0ms	(cbrt (cos (/ K 2.0)))
0.0ms	(cbrt (cos (/ K 2.0)))
1.0ms	(cbrt (cos (/ K 2.0)))
196.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series961.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (cos (/ K 2.0)))
151.0ms	(cbrt (cos (/ K 2.0)))
145.0ms	(cbrt (cos (/ K 2.0)))
514.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (cos (/ K 2.0)))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify58.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	422	1310
1	1793	930
2	5001	847

prune342.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 8.8b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cos (/ K 2.0))) (* -2.0 J))
0.1b	(* (* (* (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cos (/ K 2.0))) (* -2.0 J)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
8.5b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.5b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

36×	`pow1`
34×	`add-exp-log` `add-cbrt-cube`
21×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 86

Calls

4 calls:

14.0ms	(* (* (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cos (/ K 2.0))) (* -2.0 J))
53.0ms	(* (* (* (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cos (/ K 2.0))) (* -2.0 J)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
1.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
1.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series2.3s

Counts

4 → 12

Calls

4 calls:

668.0ms	(* (* (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cos (/ K 2.0))) (* -2.0 J))
591.0ms	(* (* (* (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))) (cos (/ K 2.0))) (* -2.0 J)) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
515.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
510.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify64.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	401	2029
1	1765	1673
2	5001	1525

prune363.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 8.8b

regimes230.0ms

Accuracy

0% (0.3b remaining)

Error of 8.5b against oracle of 8.2b and baseline of 8.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	23
1	28	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

538.0ms	7992×	body	80	valid
376.0ms	6703×	body	80	overflowed
2.0ms	10×	body	160	valid