Details

sample56.0ms

Algorithm

intervals

Results

19.0ms	54×	body	1280	valid
11.0ms	46×	body	640	valid
8.0ms	134×	body	80	valid
2.0ms	12×	body	320	valid
1.0ms	10×	body	160	valid

simplify42.0ms

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: 15.9b

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)
6.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite238.0ms

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:

17.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
20.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
138.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
60.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series566.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
140.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
190.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
143.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify64.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	543	1085
1	2466	960
2	5002	960

prune293.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.4b

localize16.0ms

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)
6.2b	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
8.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite211.0ms

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:

16.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
20.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
114.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
58.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series570.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
145.0ms	(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)))))
143.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify58.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

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

prune302.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 12.4b

localize33.0ms

Local error

Found 4 expressions with local error:

6.2b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
6.2b	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.7b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite236.0ms

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:

58.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
58.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
57.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
61.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
242.0ms	(sqrt (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
144.0ms	(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)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 3 (42.0ms)

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

prune335.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 12.4b

localize20.0ms

Local error

Found 4 expressions with local error:

2.0b	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
2.1b	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
13.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
13.2b	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite147.0ms

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:

58.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
26.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
29.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
31.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series773.0ms

Counts

4 → 12

Calls

4 calls:

225.0ms	(sqrt (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
85.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (fabs (cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))))
231.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
231.0ms	(cbrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (30.0ms)

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

prune333.0ms

Pruning

10 alts after pruning (6 fresh and 4 done)

Merged error: 12.4b

regimes340.0ms

Accuracy

45.3% (2.9b remaining)

Error of 15.6b against oracle of 12.7b and baseline of 18.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	37
1	39	37

end0.0ms

sample1.6s

Algorithm

intervals

Results

533.0ms	1477×	body	1280	valid
319.0ms	1293×	body	640	valid
284.0ms	4279×	body	80	valid
114.0ms	640×	body	320	valid
42.0ms	314×	body	160	valid