Details

analyze505.0ms (19.4%)

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

sample23.0ms (0.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
0.0ms	12×	body	80	invalid

simplify158.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	15

prune7.0ms (0.3%)

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: 27.5b

Counts

2 → 1

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
27.0b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite12.0ms (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×	`associate-/r` `associate-/l`
2×	`pow1` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv`

Counts

2 → 43

Calls

2 calls:

8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
3.0ms	(- (* x.im y.re) (* x.re y.im))

series37.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

27.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))
10.0ms	(- (* x.im y.re) (* x.re y.im))

simplify42.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5676	845

prune105.0ms (4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 23.1b

Counts

50 → 8

localize14.0ms (0.6%)

Local error

Found 4 expressions with local error:

7.4b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
8.5b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
10.7b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

rewrite34.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
38×	`times-frac`
36×	`add-cube-cbrt` `*-un-lft-identity`
30×	`associate-r`
18×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
6×	`associate-l` `associate-/r` `associate-/l`
4×	`cbrt-undiv` `flip3-+` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 126

Calls

4 calls:

11.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))

series53.0ms (2%)

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
14.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))

simplify62.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5147	1682

prune172.0ms (6.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	136	2	138
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	140	6	146

Merged error: 23.1b

Counts

146 → 6

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

8.5b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.0b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite25.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`sqrt-prod`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 93

Calls

4 calls:

9.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
5.0ms	(/ x.re (+ (* 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)))

series39.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

15.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(* y.im (/ x.re (+ (* 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)))

simplify72.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4954	1169
1	4954	1169

prune139.0ms (5.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	105	6	111

Merged error: 23.1b

Counts

111 → 6

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
16.6b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
32.2b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
32.2b	(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`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 85

Calls

4 calls:

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

series58.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
10.0ms	(- (* x.im y.re) (* x.re y.im))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))
6.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify47.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5760	1553

prune110.0ms (4.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	97	6	103

Merged error: 23.1b

Counts

103 → 6

regimes258.0ms (9.9%)

Accuracy

Total 3.6b remaining (13.7%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	33
1	50	33

end0.0ms (0%)

sample569.0ms (21.9%)

Algorithm

1×

intervals

Results

346.0ms	8000×	body	80	valid
22.0ms	517×	body	80	invalid

Details

analyze505.0ms (19.4%)

sample23.0ms (0.9%)

simplify158.0ms (6.1%)

prune7.0ms (0.3%)

localize9.0ms (0.4%)

rewrite12.0ms (0.5%)

series37.0ms (1.4%)

simplify42.0ms (1.6%)

prune105.0ms (4%)

localize14.0ms (0.6%)

rewrite34.0ms (1.3%)

series53.0ms (2%)

simplify62.0ms (2.4%)

prune172.0ms (6.6%)

localize15.0ms (0.6%)

rewrite25.0ms (1%)

series39.0ms (1.5%)

simplify72.0ms (2.8%)

prune139.0ms (5.3%)

localize12.0ms (0.5%)

rewrite22.0ms (0.9%)

series58.0ms (2.2%)

simplify47.0ms (1.8%)

prune110.0ms (4.2%)

regimes258.0ms (9.9%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

end0.0ms (0%)

sample569.0ms (21.9%)

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