Details

analyze524.0ms

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

sample43.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

prune3.0ms

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: 22.7b

Counts

2 → 1

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
22.3b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms

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:

6.0ms	(+ (* x.re y.re) (* x.im y.im))
14.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

series64.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(+ (* x.re y.re) (* x.im y.im))
47.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify61.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5169	820

prune97.0ms

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: 22.0b

Counts

49 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
13.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
27.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
27.1b	(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)))

series56.0ms

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))))
8.0ms	(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

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5503	1525

prune119.0ms

Filtered

76 candidates to 96 candidates (-26.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	95	10	105

Merged error: 20.3b

Counts

105 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.2b	(+ (* x.re y.re) (* x.im y.im))
0.5b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
22.1b	(* (+ (* 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:

3.0ms	(+ (* x.re y.re) (* x.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(* (+ (* 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:

9.0ms	(+ (* 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))))

simplify42.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4986	1322
1	4986	1322

prune104.0ms

Filtered

60 candidates to 95 candidates (-58.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	95	10	105

Merged error: 20.3b

Counts

105 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
22.1b	(* (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im)))) (sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))))
26.7b	(sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))
26.7b	(sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
31×	`times-frac`
30×	`sqrt-prod`
29×	`*-un-lft-identity`
27×	`add-cube-cbrt`
14×	`pow1` `sqrt-div`
13×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`frac-times`
7×	`flip3-+` `flip-+`
6×	`rem-sqrt-square` `sqrt-pow1` `associate-*r/` `associate-/r/`
5×	`associate-*l/`
4×	`add-log-exp`
3×	`pow-flip` `associate-l` `pow-prod-down` `prod-exp` `associate-/r` `cbrt-unprod` `div-inv` `associate-/l` `inv-pow`
2×	`pow1/2` `div-exp`
1×	`cbrt-undiv` `rec-exp` `frac-2neg` `1-exp` `associate-r` `clear-num` `*-commutative` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
23.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im)))) (sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))))
5.0ms	(sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series45.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
26.0ms	(* (+ (* x.re y.re) (* x.im y.im)) (* (sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im)))) (sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))))
7.0ms	(sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))
7.0ms	(sqrt (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify37.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5131	1897

prune144.0ms

Filtered

87 candidates to 135 candidates (-55.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	135	10	145

Merged error: 20.3b

Counts

145 → 10

regimes448.0ms

Accuracy

25.7% (2.1b remaining)

Error of 25.5b against oracle of 23.4b and baseline of 26.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	54
1	37	54

end0.0ms

sample1.4s

Algorithm

intervals

Results

363.0ms

8000×

body

valid

Details

analyze524.0ms

sample43.0ms

simplify3.0ms

prune3.0ms

localize11.0ms

rewrite22.0ms

series64.0ms

simplify61.0ms

prune97.0ms

localize12.0ms

rewrite22.0ms

series56.0ms

simplify52.0ms

prune119.0ms

localize11.0ms

rewrite25.0ms

series41.0ms

simplify42.0ms

prune104.0ms

localize14.0ms

rewrite43.0ms

series45.0ms

simplify37.0ms

prune144.0ms

regimes448.0ms

bsearch1.0ms

simplify1.0ms

end0.0ms

sample1.4s

Profiling