Details

analyze504.0ms (19.2%)

Algorithm

1×

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 (0.8%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	17×	body	80	invalid

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

prune6.0ms (0.2%)

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: 23.2b

Counts

2 → 1

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

1.0b	(+ (* x.re y.re) (* x.im y.im))
22.9b	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite13.0ms (0.5%)

Algorithm

1×	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:

8.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(+ (* x.re y.re) (* x.im y.im))

series38.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))
9.0ms	(+ (* x.re y.re) (* x.im y.im))

simplify37.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5169	820

prune100.0ms (3.8%)

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: 22.5b

Counts

49 → 9

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(+ (* 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))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite22.0ms (0.9%)

Algorithm

1×	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:

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

series56.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (+ (* x.re y.re) (* x.im y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
11.0ms	(+ (* x.re y.re) (* x.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 (2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5503	1525

prune166.0ms (6.3%)

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: 20.9b

Counts

105 → 10

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(+ (* 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))))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite23.0ms (0.9%)

Algorithm

1×	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:

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

series57.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ (+ (* 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))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify55.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5503	1525

prune137.0ms (5.2%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	96	10	106

Merged error: 20.9b

Counts

106 → 10

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

15.0b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
15.0b	(cbrt (+ (* x.re y.re) (* x.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.5b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
3.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))

series84.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(cbrt (+ (* x.re y.re) (* x.im y.im)))
35.0ms	(cbrt (+ (* x.re y.re) (* x.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)))

simplify49.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5020	738

prune83.0ms (3.2%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	68	10	78

Merged error: 20.9b

Counts

78 → 10

regimes466.0ms (17.8%)

Accuracy

Total 2.2b remaining (8.6%)

Threshold costs 0b (0%)

bsearch1.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	53
1	22	53

end0.0ms (0%)

sample581.0ms (22.1%)

Algorithm

1×

intervals

Results

354.0ms	8000×	body	80	valid
20.0ms	465×	body	80	invalid

Details

analyze504.0ms (19.2%)

sample22.0ms (0.8%)

simplify3.0ms (0.1%)

prune6.0ms (0.2%)

localize9.0ms (0.3%)

rewrite13.0ms (0.5%)

series38.0ms (1.5%)

simplify37.0ms (1.4%)

prune100.0ms (3.8%)

localize12.0ms (0.4%)

rewrite22.0ms (0.9%)

series56.0ms (2.2%)

simplify52.0ms (2%)

prune166.0ms (6.3%)

localize13.0ms (0.5%)

rewrite23.0ms (0.9%)

series57.0ms (2.2%)

simplify55.0ms (2.1%)

prune137.0ms (5.2%)

localize16.0ms (0.6%)

rewrite16.0ms (0.6%)

series84.0ms (3.2%)

simplify49.0ms (1.9%)

prune83.0ms (3.2%)

regimes466.0ms (17.8%)

bsearch1.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample581.0ms (22.1%)

Profiling