Details

sample73.0ms

Algorithm

intervals

Results

26.0ms	56×	body	1280	valid
13.0ms	131×	body	80	valid
12.0ms	33×	body	640	valid
6.0ms	22×	body	320	valid
2.0ms	14×	body	160	valid

simplify53.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 15.7b

Counts

2 → 1

localize16.0ms

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)
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
8.3b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

rewrite35.0ms

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:

5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
13.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
7.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))

series514.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
135.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
187.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))
145.0ms	(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

prune333.0ms

Filtered

108 candidates to 73 candidates (67.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	8	109

Merged error: 6.6b

Counts

109 → 8

localize18.0ms

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)))
6.4b	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite28.0ms

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:

9.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
5.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
7.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

series691.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
46.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
51.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
505.0ms	(* (* (* -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

100 → 100

Iterations

Useful iterations: 1 (14.0ms)

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

prune321.0ms

Filtered

100 candidates to 66 candidates (66.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	94	6	100
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 6.6b

Counts

108 → 9

localize17.0ms

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)))
6.4b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite23.0ms

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:

4.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
5.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
6.0ms	(* (* -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:

445.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
90.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
46.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
513.0ms	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

simplify68.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (56.0ms)

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

prune344.0ms

Filtered

101 candidates to 66 candidates (65.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	99	11	110

Merged error: 6.6b

Counts

110 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

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))))) (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)))))
6.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
6.4b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1`
27×	`add-exp-log` `add-cbrt-cube`
16×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-r` `sqrt-prod`
10×	`add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative`

Counts

4 → 85

Calls

4 calls:

11.0ms	(* (* (* (* -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)))))
7.0ms	(* (* (* -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:

527.0ms	(* (* (* (* -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)))))
573.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
518.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
505.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify68.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	399	1872
1	1830	1509
2	5002	1503

prune365.0ms

Filtered

97 candidates to 63 candidates (64.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	7	8
Picked	0	1	1
Done	1	1	2
Total	97	11	108

Merged error: 6.6b

Counts

108 → 11

regimes309.0ms

Accuracy

0% (0.3b remaining)

Error of 8.2b against oracle of 7.9b and baseline of 8.2b

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

727.0ms	1495×	body	1280	valid
442.0ms	1266×	body	640	valid
341.0ms	4264×	body	80	valid
171.0ms	656×	body	320	valid
53.0ms	322×	body	160	valid