Details

sample23.0ms

Algorithm

intervals

Results

10.0ms

272×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune2.0ms

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: 26.0b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
25.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

3×	`flip3-+` `flip-+`
2×	`associate-/r/` `associate-/l/`
1×	`+-commutative` `frac-2neg` `clear-num` `div-inv`

Counts

2 → 10

Calls

2 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series109.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
79.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify139.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	114	89
1	362	89
2	1199	89
3	3692	89
4	5003	89

prune48.0ms

Filtered

16 candidates to 13 candidates (81.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Merged error: 25.4b

Counts

17 → 6

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
0.3b	(+ (* x.re y.re) (* x.im y.im))
25.5b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

9×	`associate-/r/`
5×	`flip3-+` `flip-+`
4×	`clear-num` `associate-/l/`
3×	`frac-2neg` `associate-/r*` `div-inv`
1×	`+-commutative` `remove-double-div` `inv-pow`

Counts

3 → 23

Calls

3 calls:

8.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
8.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

series217.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
53.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	153	162
1	545	161
2	2199	158
3	5001	157

prune91.0ms

Filtered

32 candidates to 23 candidates (71.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	28	10	38

Merged error: 25.4b

Counts

38 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
0.3b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.6b	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
25.5b	(/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

23×	`associate-/r/`
11×	`flip3-+` `flip-+` `div-inv`
9×	`times-frac`
5×	`frac-2neg` `clear-num`
3×	`associate-/r` `associate-/l/` `associate-/l`
2×	`inv-pow`
1×	`+-commutative`

Counts

4 → 39

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
4.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
9.0ms	(/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* x.re y.re) (* x.im y.im))
37.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
137.0ms	(/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

simplify124.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	235	400
1	1070	376
2	4640	372
3	5001	372

prune121.0ms

Filtered

51 candidates to 34 candidates (66.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	4	3	7
Picked	0	1	1
Done	0	2	2
Total	52	9	61

Merged error: 25.3b

Counts

61 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (- (* x.re y.re) (* x.im y.im)))
0.3b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
3.9b	(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
40.8b	(* (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))) (/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (- (* x.re y.re) (* x.im y.im))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

18×	`frac-times`
14×	`associate-/r/` `associate-/l/`
13×	`flip3--` `flip--` `associate-/l*`
11×	`clear-num`
9×	`frac-2neg` `associate-r/` `-commutative`
8×	`div-inv` `difference-of-squares`
5×	`flip3-+` `flip-+`
4×	`associate-l` `un-div-inv`
3×	`associate-r`
2×	`associate-*l/`
1×	`sub-neg` `inv-pow`

Counts

4 → 66

Calls

4 calls:

8.0ms	(/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (- (* x.re y.re) (* x.im y.im)))
4.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
11.0ms	(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
23.0ms	(* (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))) (/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (- (* x.re y.re) (* x.im y.im))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (- (* x.re y.re) (* x.im y.im)))
35.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
95.0ms	(- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im)))
187.0ms	(* (- (* (* x.re y.re) (* x.re y.re)) (* (* x.im y.im) (* x.im y.im))) (/ (/ 1 (+ (* y.re y.re) (* y.im y.im))) (- (* x.re y.re) (* x.im y.im))))

simplify60.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	322	1012
1	1989	946
2	5003	926

prune166.0ms

Filtered

78 candidates to 46 candidates (59.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	2	3	5
Picked	1	0	1
Done	0	3	3
Total	78	9	87

Merged error: 25.3b

Counts

87 → 9

regimes177.0ms

Accuracy

0% (0.7b remaining)

Error of 26.1b against oracle of 25.4b and baseline of 26.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample526.0ms

Algorithm

intervals

Results

300.0ms

8441×

body

valid