Details

sample55.0ms

Algorithm

intervals

Results

15.0ms	41×	body	1280	valid
10.0ms	147×	body	80	valid
9.0ms	37×	body	640	valid
4.0ms	21×	body	320	valid
1.0ms	10×	body	160	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 15.4b

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)
5.8b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.8b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite270.0ms

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:

20.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
22.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
148.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
77.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series524.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
137.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
193.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
148.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (46.0ms)

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

prune320.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
5.8b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite114.0ms

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:

18.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
19.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
18.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
56.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series686.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
46.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
52.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
496.0ms	(* (* (* -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 (14.0ms)

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

prune321.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.1b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
5.8b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
22×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`associate-/l*`
6×	`associate-r`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`associate-l` `*-commutative`
1×	`hypot-udef` `frac-2neg` `clear-num` `associate-/l/`

Counts

4 → 103

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
19.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
15.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
56.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

series1.1s

Counts

4 → 12

Calls

4 calls:

425.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
52.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
88.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
502.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))

simplify66.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	575	1308
1	2599	1083
2	5001	1083

prune429.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
0.1b	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
0.1b	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
5.8b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
24×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
18×	`pow1`
10×	`prod-exp` `cbrt-unprod`
9×	`pow-prod-down`
7×	`associate-/l*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `associate-r` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r*`
2×	`*-commutative`
1×	`hypot-udef` `frac-2neg` `clear-num` `associate-/l/` `unswap-sqr`

Counts

4 → 104

Calls

4 calls:

0.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
10.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
15.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
28.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

434.0ms	(hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))
452.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2))))
93.0ms	(/ (/ U (* 2.0 J)) (cos (/ K 2.0)))
511.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ (/ U (* 2.0 J)) (cos (/ K 2.0))) (/ 2.0 2)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	605	1555
1	2672	1277
2	5002	1276

prune413.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.9b

regimes312.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.8b and baseline of 8.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	14
1	23	14

end0.0ms

sample1.6s

Algorithm

intervals

Results

560.0ms	1489×	body	1280	valid
310.0ms	1216×	body	640	valid
297.0ms	4381×	body	80	valid
121.0ms	610×	body	320	valid
40.0ms	307×	body	160	valid