Details

sample89.0ms

Algorithm

intervals

Results

35.0ms	58×	body	1280	valid
18.0ms	41×	body	640	valid
12.0ms	133×	body	80	valid
5.0ms	15×	body	320	valid
2.0ms	9×	body	160	valid

simplify46.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

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: 16.7b

Counts

2 → 1

localize17.0ms

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)
7.6b	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
8.1b	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-exp-log`
22×	`add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`pow1`
12×	`add-cube-cbrt` `prod-exp`
9×	`cbrt-unprod`
8×	`unpow-prod-down` `sqrt-prod`
7×	`associate-r`
6×	`times-frac` `div-exp` `pow-prod-down`
4×	`expm1-log1p-u` `sqrt-div` `pow-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `hypot-def` `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` `associate-l` `clear-num` `associate-/r` `-commutative`

Counts

4 → 101

Calls

4 calls:

6.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
8.0ms	(pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)
8.0ms	(sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0)))
19.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

series569.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
140.0ms	(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)))
194.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (+ 1.0 (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) 2.0))))

simplify68.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	555	1156
1	2493	1029
2	5001	1028

prune344.0ms

Filtered

113 candidates to 78 candidates (69.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Merged error: 8.4b

Counts

114 → 7

localize19.0ms

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))))
8.1b	(* (* (* -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:

5.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
5.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
6.0ms	(/ U (* (* 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))))

series705.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
49.0ms	(* (* -2.0 J) (cos (/ K 2.0)))
91.0ms	(/ U (* (* 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))))

simplify65.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (13.0ms)

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

prune304.0ms

Filtered

100 candidates to 66 candidates (66.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	99	8	107

Merged error: 8.4b

Counts

107 → 8

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	(* (* 2.0 J) (cos (/ K 2.0)))
0.1b	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
8.1b	(* (* -2.0 J) (* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))

rewrite24.0ms

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))))
5.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
6.0ms	(/ U (* (* 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:

450.0ms	(* (cos (/ K 2.0)) (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
51.0ms	(* (* 2.0 J) (cos (/ K 2.0)))
93.0ms	(/ U (* (* 2.0 J) (cos (/ K 2.0))))
510.0ms	(* (* -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

prune302.0ms

Filtered

101 candidates to 66 candidates (65.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	99	10	109

Merged error: 8.4b

Counts

109 → 10

localize26.0ms

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)))))
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)))))
8.1b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
8.1b	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

rewrite26.0ms

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:

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

567.0ms	(* (* (* -2.0 J) (cos (/ K 2.0))) (sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2)))))
514.0ms	(* (* (* (* -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)))))
507.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))
517.0ms	(sqrt (hypot (sqrt 1.0) (pow (/ U (* (* 2.0 J) (cos (/ K 2.0)))) (/ 2.0 2))))

simplify62.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	399	1872
1	1829	1509
2	5001	1503

prune328.0ms

Filtered

97 candidates to 64 candidates (66.0%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	7	7
Picked	0	1	1
Done	1	1	2
Total	96	11	107

Merged error: 8.3b

Counts

107 → 11

regimes374.0ms

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

sample2.4s

Algorithm

intervals

Results

951.0ms	1521×	body	1280	valid
573.0ms	1252×	body	640	valid
397.0ms	4338×	body	80	valid
194.0ms	593×	body	320	valid
70.0ms	299×	body	160	valid