Details

analyze532.0ms

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

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	16×	body	80	invalid

simplify164.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (163.0ms)

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: 25.3b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.5b	(- (* x.im y.re) (* x.re y.im))
24.9b	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
3.0ms	(- (* 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)))

series47.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(- (* x.im y.re) (* x.re y.im))
31.0ms	(/ (- (* x.im y.re) (* x.re y.im)) (+ (* y.re y.re) (* y.im y.im)))

simplify48.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5785	976

prune100.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	8	64

Merged error: 20.7b

Counts

64 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* x.im y.re) (* x.re y.im))
17.3b	(/ (- (* x.im y.re) (* x.re y.im)) (sqrt (+ (* y.re y.re) (* y.im y.im))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(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)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (* 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)))

simplify48.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5760	1553

prune127.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 20.7b

Counts

105 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

10.5b	(* y.re (/ x.im (sqrt (+ (* y.re y.re) (* y.im y.im)))))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))
29.0b	(sqrt (+ (* y.re y.re) (* y.im y.im)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
24×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`sqrt-prod`
9×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`sqrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `unswap-sqr`
2×	`prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `associate-r/` `div-exp` `pow-prod-down` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

11.0ms	(* y.re (/ x.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)))
4.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* y.re (/ x.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)))
8.0ms	(sqrt (+ (* y.re y.re) (* y.im y.im)))

simplify37.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5040	1084

prune122.0ms

Filtered

75 candidates to 101 candidates (-34.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	101	10	111

Merged error: 20.7b

Counts

111 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* y.re y.re) (* y.im y.im))
0.3b	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
0.5b	(- (* x.im y.re) (* x.re y.im))
24.8b	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`flip3--` `flip3-+` `associate-l` `associate-/r` `flip--` `flip-+` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`+-commutative` `sub-neg` `pow-flip` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+ (* y.re y.re) (* y.im y.im))
5.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
4.0ms	(- (* x.im y.re) (* x.re y.im))
12.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (* y.re y.re) (* y.im y.im))
10.0ms	(/ 1 (+ (* y.re y.re) (* y.im y.im)))
18.0ms	(- (* x.im y.re) (* x.re y.im))
29.0ms	(* (- (* x.im y.re) (* x.re y.im)) (/ 1 (+ (* y.re y.re) (* y.im y.im))))

simplify47.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5226	1457

prune88.0ms

Filtered

72 candidates to 109 candidates (-51.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	109	10	119

Merged error: 20.7b

Counts

119 → 10

regimes322.0ms

Accuracy

-33.3% (1.5b remaining)

Error of 23.2b against oracle of 21.7b and baseline of 22.8b

bsearch36.0ms

Steps

Iters	Range		Point
8	8.160637474362413e-100	4.053124885802596e-95	2.547251396127817e-98
8	-2.5116001733608297e-07	-3.9050042177072455e-10	-1.936337481574621e-09

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	68
1	78	68

end0.0ms

sample589.0ms

Algorithm

intervals

Results

354.0ms	8000×	body	80	valid
19.0ms	463×	body	80	invalid

Details

analyze532.0ms

sample23.0ms

simplify164.0ms

prune4.0ms

localize10.0ms

rewrite17.0ms

series47.0ms

simplify48.0ms

prune100.0ms

localize12.0ms

rewrite22.0ms

series58.0ms

simplify48.0ms

prune127.0ms

localize14.0ms

rewrite26.0ms

series33.0ms

simplify37.0ms

prune122.0ms

localize11.0ms

rewrite27.0ms

series62.0ms

simplify47.0ms

prune88.0ms

regimes322.0ms

bsearch36.0ms

simplify2.0ms

end0.0ms

sample589.0ms

Profiling