Details

analyze553.0ms

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

sample24.0ms

Algorithm

intervals

Results

12.0ms	256×	body	80	valid
1.0ms	21×	body	80	invalid

simplify166.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4841	15
1	4841	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.im y.re) (* x.re y.im))
26.1b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite16.0ms

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×	`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:

7.0ms	(- (* x.im y.re) (* x.re y.im))
8.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

series37.0ms

Counts

2 → 6

Calls

2 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5676	845

prune90.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

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: 22.3b

Counts

50 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

7.7b	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
8.0b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.7b	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
9.8b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

rewrite31.0ms

Algorithm

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:

5.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(* 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))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(/ x.im (+ (* y.re y.re) (* y.im y.im)))
13.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* y.re (/ x.im (+ (* y.re y.re) (* y.im y.im))))
13.0ms	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))

simplify59.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5147	1682

prune153.0ms

Filtered

104 candidates to 138 candidates (-32.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	1	138
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	138	8	146

Merged error: 22.3b

Counts

146 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

8.0b	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
9.8b	(* y.im (/ x.re (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite24.0ms

Algorithm

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:

5.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
8.0ms	(* y.im (/ 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)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ x.re (+ (* y.re y.re) (* y.im y.im)))
12.0ms	(* 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)))

simplify75.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4954	1169
1	4954	1169

prune128.0ms

Filtered

82 candidates to 105 candidates (-28.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	1	105
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 22.3b

Counts

113 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* x.im y.re) (* x.re y.im))
18.7b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
30.1b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
30.1b	(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`
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:

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify54.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5760	1553

prune95.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	97	8	105

Merged error: 22.3b

Counts

105 → 8

regimes315.0ms

Accuracy

23% (2.3b remaining)

Error of 24.1b against oracle of 21.8b and baseline of 24.7b

bsearch27.0ms

Steps

Iters	Range		Point
4	1.5090686683113488e-237	2.3460906902379327e-237	1.9014227410894348e-237
7	-9.698438444323529e-76	-2.3998280062687315e-77	-2.870423058279664e-77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	67
1	78	67

end0.0ms

sample585.0ms

Algorithm

intervals

Results

361.0ms	8000×	body	80	valid
19.0ms	443×	body	80	invalid

Details

analyze553.0ms

sample24.0ms

simplify166.0ms

prune4.0ms

localize10.0ms

rewrite16.0ms

series37.0ms

simplify46.0ms

prune90.0ms

localize12.0ms

rewrite31.0ms

series54.0ms

simplify59.0ms

prune153.0ms

localize17.0ms

rewrite24.0ms

series38.0ms

simplify75.0ms

prune128.0ms

localize15.0ms

rewrite22.0ms

series55.0ms

simplify54.0ms

prune95.0ms

regimes315.0ms

bsearch27.0ms

simplify2.0ms

end0.0ms

sample585.0ms

Profiling