Details

sample62.0ms

Algorithm

intervals

Results

20.0ms	56×	body	1280	valid
12.0ms	47×	body	640	valid
9.0ms	124×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	9×	body	160	valid

simplify47.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.3b	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
5.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
9.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite257.0ms

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:

19.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
21.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
142.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
72.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
121.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
175.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
129.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (51.0ms)

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

prune330.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.7b

localize19.0ms

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)))
5.5b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite109.0ms

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:

17.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
18.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
18.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
54.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series635.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
47.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
41.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
470.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify71.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (14.0ms)

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

prune316.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize19.0ms

Local error

Found 4 expressions with local error:

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))))
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
5.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 89

Calls

4 calls:

8.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
17.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
17.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
31.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

series993.0ms

Counts

4 → 12

Calls

4 calls:

407.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
83.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
47.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
456.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	524	1240
1	2426	964
2	5002	963

prune321.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* (* 2.0 J) (cos (/ K 2.0))) U)
0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.5b	(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
5.6b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2)))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
44×	`add-cbrt-cube`
36×	`times-frac`
23×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `prod-exp`
22×	`pow1`
20×	`div-exp`
17×	`cbrt-unprod`
11×	`pow-prod-down`
10×	`cbrt-undiv` `associate-/r*`
6×	`div-inv`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `log1p-expm1-u` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`pow-flip` `associate-/r/` `inv-pow`

Counts

4 → 131

Calls

4 calls:

21.0ms	(/ (* (* 2.0 J) (cos (/ K 2.0))) U)
17.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
29.0ms	(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
26.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2)))))

series661.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(/ (* (* 2.0 J) (cos (/ K 2.0))) U)
46.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
84.0ms	(/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U))
460.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ 1 (/ (* (* 2.0 J) (cos (/ K 2.0))) U)) (/ 2.0 2)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	665	1522
1	3430	1207
2	5003	1174

prune356.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.6b

regimes287.0ms

Accuracy

0% (0.3b remaining)

Error of 8.1b against oracle of 7.9b and baseline of 8.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample1.7s

Algorithm

intervals

Results

566.0ms	1533×	body	1280	valid
331.0ms	1274×	body	640	valid
300.0ms	4230×	body	80	valid
123.0ms	648×	body	320	valid
42.0ms	322×	body	160	valid