Details

sample26.0ms

Algorithm

intervals

Results

11.0ms

277×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

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: 23.6b

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))
23.2b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
11.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series41.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
26.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify123.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4437	477
3	5002	477

prune110.0ms

Filtered

62 candidates to 49 candidates (21.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 23.0b

Counts

63 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
12.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* x.re y.re) (* x.im y.im))
33.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (21.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune125.0ms

Filtered

96 candidates to 74 candidates (22.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	93	13	106

Merged error: 21.7b

Counts

106 → 13

localize11.0ms

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))))
22.8b	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

3.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(+ (* x.re y.re) (* x.im y.im))
9.0ms	(/ 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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
9.0ms	(+ (* x.re y.re) (* x.im y.im))
27.0ms	(/ 1 (/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im))))
18.0ms	(/ (+ (* y.re y.re) (* y.im y.im)) (+ (* x.re y.re) (* x.im y.im)))

simplify64.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	518	1819
1	2632	1654
2	5001	1567

prune129.0ms

Filtered

149 candidates to 84 candidates (43.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	3	8	11
Picked	1	0	1
Done	0	1	1
Total	151	11	162

Merged error: 21.7b

Counts

162 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))))
12.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
26.3b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

1473×	`times-frac`
681×	`add-sqr-sqrt`
679×	`add-cube-cbrt` `*-un-lft-identity`
522×	`sqrt-prod`
155×	`associate-/r*`
55×	`associate-/r/`
54×	`sqrt-div`
30×	`div-inv`
28×	`flip3-+` `flip-+`
27×	`add-exp-log`
16×	`div-exp`
15×	`add-cbrt-cube`
7×	`pow1` `cbrt-undiv`
6×	`associate-/l*`
4×	`add-log-exp`
3×	`rec-exp` `1-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 697

Calls

4 calls:

36.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))))
9.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1 (/ (sqrt (+ (* y.re y.re) (* y.im y.im))) (/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))))
39.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify186.0ms

Algorithm

egg-herbie

Counts

709 → 709

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2010	18819
1	5001	17287

prune371.0ms

Filtered

709 candidates to 288 candidates (59.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	708	1	709
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	708	12	720

Merged error: 21.7b

Counts

720 → 12

regimes479.0ms

Accuracy

0% (2.2b remaining)

Error of 25.9b against oracle of 23.7b and baseline of 25.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

sample730.0ms

Algorithm

intervals

Results

365.0ms

8492×

body

valid

Details

sample26.0ms

simplify3.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series41.0ms

simplify123.0ms

prune110.0ms

localize11.0ms

rewrite23.0ms

series53.0ms

simplify77.0ms

prune125.0ms

localize11.0ms

rewrite29.0ms

series59.0ms

simplify64.0ms

prune129.0ms

localize14.0ms

rewrite121.0ms

series77.0ms

simplify186.0ms

prune371.0ms

regimes479.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample730.0ms

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