Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

265×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	21	7
2	21	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: 27.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
26.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

4×	`fma-def` `flip3-+` `flip-+`
2×	`+-commutative` `associate-/r/` `*-commutative` `associate-/l/`
1×	`frac-2neg` `clear-num` `div-inv`

Counts

3 → 17

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
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)))

series139.0ms

Counts

3 → 9

Calls

3 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
80.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	157	113
1	640	106
2	2288	102
3	5001	100

prune78.0ms

Filtered

26 candidates to 19 candidates (73.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	20	6	26
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	7	27

Merged error: 26.7b

Counts

27 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.4b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

8×	`flip3-+` `flip-+`
6×	`frac-times`
5×	`clear-num`
4×	`fma-def` `frac-2neg` `associate-/r/`
3×	`associate-r/` `associate-r` `-commutative`
2×	`+-commutative` `associate-*l/` `un-div-inv` `div-inv`
1×	`inv-pow`

Counts

4 → 33

Calls

4 calls:

7.0ms	(+ (* y.re y.re) (* y.im y.im))
4.0ms	(+ (* x.re y.re) (* x.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* y.re y.re) (* y.im y.im))
29.0ms	(+ (* x.re y.re) (* x.im y.im))
40.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
76.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify33.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	200	217
1	960	210
2	5001	206

prune108.0ms

Filtered

45 candidates to 29 candidates (64.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	45	7	52

Merged error: 26.7b

Counts

52 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(+ (* x.re y.re) (* x.im y.im))
0.7b	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
26.3b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 30

Calls

4 calls:

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

series250.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* y.re y.re) (* y.im y.im))
30.0ms	(+ (* x.re y.re) (* x.im y.im))
138.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
52.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify100.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 3 (95.0ms)

Iter	Nodes	Cost
0	175	182
1	774	167
2	3585	155
3	5002	153

prune129.0ms

Filtered

42 candidates to 31 candidates (73.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	42	7	49

Merged error: 26.7b

Counts

49 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
0.6b	(/ 1 (fma y.re y.re (* y.im y.im)))
0.8b	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
26.1b	(/ (/ 1 (fma y.re y.re (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 31

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
2.0ms	(/ 1 (fma y.re y.re (* y.im y.im)))
5.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
7.0ms	(/ (/ 1 (fma y.re y.re (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* x.re y.re) (* x.im y.im))
48.0ms	(/ 1 (fma y.re y.re (* y.im y.im)))
26.0ms	(/ 1 (+ (* x.re y.re) (* x.im y.im)))
148.0ms	(/ (/ 1 (fma y.re y.re (* y.im y.im))) (/ 1 (+ (* x.re y.re) (* x.im y.im))))

simplify66.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	137	175
1	557	161
2	2162	160
3	5001	160

prune92.0ms

Filtered

43 candidates to 28 candidates (65.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	43	0	43
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	43	7	50

Merged error: 26.7b

Counts

50 → 7

regimes152.0ms

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

sample578.0ms

Algorithm

intervals

Results

337.0ms

8478×

body

valid