Details

analyze533.0ms

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

sample22.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	14×	body	80	invalid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune1.0ms

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: 24.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.7b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
24.0b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
9.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series155.0ms

Counts

3 → 9

Calls

3 calls:

20.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
37.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
97.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify62.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5215	1768

prune90.0ms

Filtered

50 candidates to 62 candidates (-24.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 23.8b

Counts

63 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
12.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
29.4b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
29.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64`
28×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 94

Calls

4 calls:

4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
122.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
26.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify92.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5448	3187

prune122.0ms

Filtered

77 candidates to 106 candidates (-37.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	98	8	106
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	103	13	116

Merged error: 21.8b

Counts

116 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
12.3b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
29.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
29.4b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
30×	`sqrt-prod_binary64`
25×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
8×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 96

Calls

4 calls:

4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
14.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
10.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

series208.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
125.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify69.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4985	3217
1	4985	3217

prune136.0ms

Filtered

76 candidates to 108 candidates (-42.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	107	14	121

Merged error: 21.8b

Counts

121 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.3b	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
0.7b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
23.9b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

140×	`*-un-lft-identity_binary64`
138×	`times-frac_binary64`
72×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
34×	`distribute-lft-out_binary64` `unpow-prod-down_binary64`
24×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`flip3-+_binary64` `add-log-exp_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
6×	`div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `sum-log_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64`

Counts

4 → 171

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
15.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
13.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
122.0ms	(/.f64 1 (/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im))))
35.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
62.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

simplify152.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4946	7314
1	4946	7314

prune139.0ms

Filtered

105 candidates to 183 candidates (-74.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	182	15	197

Merged error: 21.8b

Counts

197 → 15

regimes117.0ms

Accuracy

0% (2.9b remaining)

Error of 26.1b against oracle of 23.2b and baseline of 26.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	49
1	26	49

end0.0ms

sample588.0ms

Algorithm

intervals

Results

357.0ms	8000×	body	80	valid
20.0ms	466×	body	80	invalid

Details

analyze533.0ms

sample22.0ms

simplify16.0ms

prune1.0ms

localize11.0ms

rewrite19.0ms

series155.0ms

simplify62.0ms

prune90.0ms

localize19.0ms

rewrite33.0ms

series213.0ms

simplify92.0ms

prune122.0ms

localize16.0ms

rewrite39.0ms

series208.0ms

simplify69.0ms

prune136.0ms

localize13.0ms

rewrite50.0ms

series238.0ms

simplify152.0ms

prune139.0ms

regimes117.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample588.0ms

Profiling