Details

sample39.0ms

Algorithm

intervals

Results

20.0ms

265×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

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: 27.3b

Counts

2 → 1

localize18.0ms

Local error

Found 2 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
26.7b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

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))
13.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series108.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(+ (* 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)))

simplify80.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 2 (22.0ms)

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

prune125.0ms

Filtered

48 candidates to 38 candidates (79.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	41	7	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	8	49

Merged error: 26.5b

Counts

49 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
16.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
35.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify82.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

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

prune234.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	95	9	104

Merged error: 23.8b

Counts

104 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(+ (* x.re y.re) (* x.im y.im))
16.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(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)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+ (* x.re y.re) (* x.im y.im))
104.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
37.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify78.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (22.0ms)

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

prune234.0ms

Filtered

96 candidates to 74 candidates (77.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	96	9	105

Merged error: 23.8b

Counts

105 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

16.6b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.7b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
38.8b	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
24×	`sqrt-prod`
18×	`cbrt-prod` `times-frac`
8×	`sqrt-div`
6×	`pow1` `add-exp-log` `unpow-prod-down` `cube-prod` `associate-/r*` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`associate-/l*`
2×	`cube-div` `rem-sqrt-square` `cbrt-div` `sqrt-pow1` `pow1/2` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `frac-2neg` `pow1/3` `unpow3` `div-exp` `clear-num` `rem-cbrt-cube` `div-inv` `sqr-pow`

Counts

4 → 102

Calls

4 calls:

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)))
3.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

series236.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
34.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
36.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
34.0ms	(cbrt (pow (sqrt (+ (* y.re y.re) (* y.im y.im))) 3))

simplify41.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	340	1014
1	1338	937
2	5001	934

prune268.0ms

Filtered

114 candidates to 81 candidates (71.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	113	10	123

Merged error: 23.8b

Counts

123 → 10

regimes195.0ms

Accuracy

24.5% (2.3b remaining)

Error of 25.1b against oracle of 22.8b and baseline of 25.9b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	26
1	27	26

end0.0ms

sample657.0ms

Algorithm

intervals

Results

402.0ms

8493×

body

valid

Details

sample39.0ms

simplify6.0ms

prune4.0ms

localize18.0ms

rewrite17.0ms

series108.0ms

simplify80.0ms

prune125.0ms

localize11.0ms

rewrite22.0ms

series205.0ms

simplify82.0ms

prune234.0ms

localize15.0ms

rewrite22.0ms

series209.0ms

simplify78.0ms

prune234.0ms

localize14.0ms

rewrite27.0ms

series236.0ms

simplify41.0ms

prune268.0ms

regimes195.0ms

bsearch2.0ms

simplify1.0ms

end0.0ms

sample657.0ms

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