Details

analyze709.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	12×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

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: 26.6b

Counts

2 → 1

localize10.0ms

Local error

Found 2 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
26.1b	(/ (+ (* 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:

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)))

series39.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(+ (* 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)))

simplify37.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5169	820

prune76.0ms

Filtered

38 candidates to 48 candidates (-26.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	43	5	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	5	49

Merged error: 25.8b

Counts

49 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
14.5b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
31.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.1b	(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:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
34.0ms	(/ (+ (* 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5503	1525

prune110.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	94	7	101

Merged error: 24.6b

Counts

101 → 7

localize10.0ms

Local error

Found 3 expressions with local error:

0.3b	(+ (* x.re y.re) (* x.im y.im))
0.7b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
25.5b	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
19×	`add-cube-cbrt`
16×	`add-exp-log`
15×	`associate-r`
10×	`add-cbrt-cube`
6×	`pow1`
5×	`flip3-+` `flip-+` `add-log-exp`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

3 → 86

Calls

3 calls:

4.0ms	(+ (* x.re y.re) (* x.im y.im))
7.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series41.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(+ (* x.re y.re) (* x.im y.im))
6.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify43.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4986	1322
1	4986	1322

prune93.0ms

Filtered

62 candidates to 95 candidates (-53.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Merged error: 24.6b

Counts

102 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

8.4b	(/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (sqrt (+ (* y.re y.re) (* y.im y.im)))))
31.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
31.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod`
32×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
27×	`times-frac`
10×	`sqrt-div`
9×	`associate-/r*`
7×	`pow1`
6×	`add-exp-log` `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 → 100

Calls

4 calls:

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(/ (+ (* y.re x.re) (* y.im x.im)) (sqrt (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)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5712	1977

prune100.0ms

Filtered

81 candidates to 112 candidates (-38.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	112	7	119

Merged error: 24.6b

Counts

119 → 7

regimes261.0ms

Accuracy

0% (3.1b remaining)

Error of 26.6b against oracle of 23.5b and baseline of 26.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	25
1	17	25

end0.0ms

sample568.0ms

Algorithm

intervals

Results

343.0ms	8000×	body	80	valid
20.0ms	485×	body	80	invalid

Details

analyze709.0ms

sample22.0ms

simplify3.0ms

prune4.0ms

localize10.0ms

rewrite13.0ms

series39.0ms

simplify37.0ms

prune76.0ms

localize12.0ms

rewrite22.0ms

series58.0ms

simplify54.0ms

prune110.0ms

localize10.0ms

rewrite25.0ms

series41.0ms

simplify43.0ms

prune93.0ms

localize14.0ms

rewrite24.0ms

series103.0ms

simplify55.0ms

prune100.0ms

regimes261.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample568.0ms

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