Details

sample69.0ms

Algorithm

intervals

Results

21.0ms	47×	body	1280	valid
14.0ms	139×	body	80	valid
14.0ms	44×	body	640	valid
4.0ms	16×	body	320	valid
2.0ms	10×	body	160	valid

simplify49.0ms

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	1364	13
6	5002	13

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 19.1b

Counts

2 → 1

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)
8.5b	(* (* (* -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)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

186×	`add-sqr-sqrt`
142×	`associate-l`
135×	`times-frac`
98×	`*-un-lft-identity`
94×	`add-cube-cbrt`
74×	`unpow-prod-down`
55×	`associate-r`
47×	`unswap-sqr`
32×	`add-exp-log`
22×	`associate-/r*` `add-cbrt-cube`
17×	`*-commutative`
15×	`pow1`
12×	`prod-exp`
11×	`sqrt-prod`
9×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down` `hypot-def`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `associate-*r/` `flip-+` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 278

Calls

4 calls:

13.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
17.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
44.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
30.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series577.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
138.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
200.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (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)))

simplify70.0ms

Algorithm

egg-herbie

Counts

290 → 290

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1280	3241
1	5002	3114

prune795.0ms

Filtered

290 candidates to 218 candidates (24.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	282	8	290
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	283	8	291

Merged error: 8.8b

Counts

291 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(* (* -2.0 J) (cos (/ K 2.0)))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
8.5b	(* (* (* -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

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

Counts

4 → 222

Calls

4 calls:

12.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
8.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
14.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
14.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series710.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
49.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
90.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
519.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify108.0ms

Algorithm

egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	891	2326
1	3897	2103
2	5001	2103

prune859.0ms

Filtered

234 candidates to 175 candidates (25.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	228	6	234
Fresh	6	1	7
Picked	0	1	1
Done	0	0	0
Total	234	8	242

Merged error: 8.8b

Counts

242 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
0.2b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
8.6b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.6b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

127×	`add-sqr-sqrt`
113×	`associate-l`
70×	`unswap-sqr`
34×	`sqrt-prod`
30×	`associate-r`
29×	`pow1`
27×	`add-exp-log` `add-cbrt-cube`
23×	`add-cube-cbrt` `*-un-lft-identity`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 164

Calls

4 calls:

25.0ms	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
15.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (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))))

series2.1s

Counts

4 → 12

Calls

4 calls:

517.0ms	(* (* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
566.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
506.0ms	(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))))

simplify91.0ms

Algorithm

egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	576	3910
1	2236	3235
2	5002	3209

prune511.0ms

Filtered

176 candidates to 117 candidates (33.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	175	1	176
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	176	8	184

Merged error: 8.8b

Counts

184 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
8.5b	(* (* (* (* -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))))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

419×	`add-sqr-sqrt`
295×	`unswap-sqr`
194×	`associate-l`
126×	`cbrt-prod`
91×	`add-cbrt-cube` `cbrt-unprod`
45×	`associate-r`
29×	`pow1` `add-exp-log`
26×	`swap-sqr`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow-prod-down` `prod-exp`
15×	`*-commutative`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`

Counts

4 → 237

Calls

4 calls:

2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
56.0ms	(* (* (* (* -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))))

series974.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (cos (/ K 2.0)))
148.0ms	(cbrt (cos (/ K 2.0)))
151.0ms	(cbrt (cos (/ K 2.0)))
523.0ms	(* (* (* (* -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))))

simplify167.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1211	6775
1	4914	5495
2	5001	5495

prune746.0ms

Filtered

249 candidates to 166 candidates (33.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	248	9	257

Merged error: 8.8b

Counts

257 → 9

regimes255.0ms

Accuracy

0% (0.3b remaining)

Error of 7.8b against oracle of 7.5b and baseline of 7.8b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample1.9s

Algorithm

intervals

Results

713.0ms	1507×	body	1280	valid
433.0ms	1299×	body	640	valid
314.0ms	4251×	body	80	valid
150.0ms	622×	body	320	valid
51.0ms	330×	body	160	valid