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

simplify45.0ms

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	1352	13
6	5001	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)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

169×	`add-sqr-sqrt`
142×	`associate-l`
132×	`times-frac`
98×	`*-un-lft-identity`
94×	`add-cube-cbrt`
70×	`unpow-prod-down`
55×	`associate-r`
44×	`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`
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` `clear-num` `sqr-pow`

Counts

4 → 264

Calls

4 calls:

14.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
16.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
43.0ms	(* (* (* -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)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
140.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
204.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
155.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify66.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1268	3170
1	5001	3045

prune771.0ms

Filtered

276 candidates to 204 candidates (26.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	268	8	276
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	268	9	277

Merged error: 12.9b

Counts

277 → 9

localize18.0ms

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	(* J (* (* -2.0 (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)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

172×	`add-sqr-sqrt`
132×	`times-frac`
123×	`associate-l`
98×	`*-un-lft-identity`
94×	`add-cube-cbrt`
80×	`associate-r`
70×	`unpow-prod-down`
46×	`unswap-sqr`
32×	`add-exp-log`
22×	`associate-/r*` `add-cbrt-cube`
17×	`*-commutative`
15×	`pow1`
12×	`prod-exp` `sqrt-prod`
9×	`cbrt-unprod`
6×	`div-exp` `pow-prod-down`
4×	`sqrt-div` `associate-*r/` `pow-exp` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/l*`
2×	`flip3-+` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sqr-pow`

Counts

4 → 265

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)
46.0ms	(* J (* (* -2.0 (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)))

series608.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
146.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
206.0ms	(* J (* (* -2.0 (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
159.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify68.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1293	3058
1	5001	2932

prune755.0ms

Filtered

277 candidates to 201 candidates (27.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	273	4	277
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	277	9	286

Merged error: 12.9b

Counts

286 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (cos (/ K 2.0)))
8.6b	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (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)))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

538×	`add-sqr-sqrt`
390×	`unswap-sqr`
137×	`cbrt-prod`
126×	`add-cbrt-cube`
124×	`cbrt-unprod`
89×	`associate-l`
65×	`associate-r`
48×	`sqrt-prod`
46×	`pow1`
45×	`add-exp-log`
31×	`pow-prod-down` `prod-exp`
30×	`swap-sqr`
29×	`*-un-lft-identity`
25×	`add-cube-cbrt`
17×	`*-commutative`
4×	`sqrt-div` `associate-*r/` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 280

Calls

4 calls:

2.0ms	(cbrt (cos (/ K 2.0)))
2.0ms	(cbrt (cos (/ K 2.0)))
83.0ms	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (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)))

series671.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (cos (/ K 2.0)))
149.0ms	(cbrt (cos (/ K 2.0)))
206.0ms	(* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (* (cbrt (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
160.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify96.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1143	8977
1	5001	7684

prune670.0ms

Filtered

292 candidates to 156 candidates (46.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	289	3	292
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	290	11	301

Merged error: 12.9b

Counts

301 → 11

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (cos (/ K 2.0)))
0.3b	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
8.6b	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (* (cbrt (cbrt (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)))

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

9075×	`add-sqr-sqrt`
7465×	`unswap-sqr`
4518×	`cbrt-prod`
646×	`swap-sqr`
584×	`sqrt-prod`
391×	`associate-l`
322×	`*-commutative`
319×	`cbrt-unprod`
288×	`add-cbrt-cube`
112×	`associate-r`
61×	`pow1`
60×	`add-exp-log`
49×	`*-un-lft-identity`
45×	`add-cube-cbrt`
44×	`pow-prod-down` `prod-exp`
4×	`sqrt-div` `associate-*r/` `add-log-exp`
2×	`flip3-+` `pow1/3` `flip-+` `distribute-lft-out`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 1816

Calls

4 calls:

2.0ms	(cbrt (cos (/ K 2.0)))
8.0ms	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
219.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (* (cbrt (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
29.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series695.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (cos (/ K 2.0)))
176.0ms	(cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))
208.0ms	(* (* (* (* -2.0 J) (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))) (cbrt (* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0)))))) (* (cbrt (cbrt (cos (/ K 2.0)))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))))
160.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

simplify818.0ms

Algorithm

egg-herbie

Counts

1828 → 1828

Iterations

Useful iterations: 1 (68.0ms)

Iter	Nodes	Cost
0	4021	106042
1	5002	104862

prune2.9s

Filtered

1828 candidates to 485 candidates (73.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	1827	1	1828
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	1828	11	1839

Merged error: 12.9b

Counts

1839 → 11

regimes337.0ms

Accuracy

83.3% (1.0b remaining)

Error of 13.3b against oracle of 12.3b and baseline of 18.2b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	50
1	49	50

end0.0ms

sample1.9s

Algorithm

intervals

Results

722.0ms	1507×	body	1280	valid
444.0ms	1299×	body	640	valid
330.0ms	4251×	body	80	valid
152.0ms	622×	body	320	valid
53.0ms	330×	body	160	valid