Details

sample27.0ms

Algorithm

intervals

Results

11.0ms

268×

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

prune4.0ms

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: 27.7b

Counts

2 → 1

localize14.0ms

Local error

Found 2 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
27.1b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 42

Calls

2 calls:

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

series38.0ms

Counts

2 → 6

Calls

2 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
28.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify84.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	231	450
1	847	413
2	2837	412
3	5001	412

prune93.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	40	8	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	40	9	49

Merged error: 26.8b

Counts

49 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
17.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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))
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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
37.0ms	(/ (+ (* 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)))

simplify83.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (23.0ms)

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

prune120.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	95	10	105

Merged error: 25.3b

Counts

105 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (* x.re y.re) (* x.im y.im))
17.4b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (sqrt (+ (* y.re y.re) (* y.im y.im)))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
5×	`unswap-sqr`
4×	`prod-exp`
3×	`associate-l`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 94

Calls

4 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
15.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
36.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (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)))

simplify52.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	385	911
1	1913	826
2	5002	802

prune121.0ms

Filtered

75 candidates to 106 candidates (-41.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	106	10	116

Merged error: 25.3b

Counts

116 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

17.4b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.4b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(/ (+ (* 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)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify72.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	242	919
1	758	870
2	2262	857
3	5002	857

prune89.0ms

Filtered

78 candidates to 100 candidates (-28.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	99	11	110

Merged error: 25.3b

Counts

110 → 11

regimes477.0ms

Accuracy

25.7% (2.2b remaining)

Error of 25.5b against oracle of 23.3b and baseline of 26.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample735.0ms

Algorithm

intervals

Results

362.0ms

8509×

body

valid

Details

sample27.0ms

simplify3.0ms

prune4.0ms

localize14.0ms

rewrite13.0ms

series38.0ms

simplify84.0ms

prune93.0ms

localize12.0ms

rewrite22.0ms

series59.0ms

simplify83.0ms

prune120.0ms

localize13.0ms

rewrite29.0ms

series59.0ms

simplify52.0ms

prune121.0ms

localize14.0ms

rewrite23.0ms

series54.0ms

simplify72.0ms

prune89.0ms

regimes477.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample735.0ms

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