Details

analyze526.0ms

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

simplify191.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (188.0ms)

Iter	Nodes	Cost
0	4821	15
1	4821	15

prune3.0ms

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: 26.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
25.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite22.0ms

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`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
13.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series48.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
11.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
31.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify50.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5785	976

prune65.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	55	8	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	9	64

Merged error: 25.6b

Counts

64 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
16.3b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
29.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
29.8b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
10.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
39.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))))
6.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
7.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify49.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5760	1553

prune64.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	96	10	106

Merged error: 23.5b

Counts

106 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.6b	(/.f64 1 (/.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)) (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))))
25.6b	(/.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)) (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
56×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `div-exp_binary64`
6×	`flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `inv-pow_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 137

Calls

4 calls:

4.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
11.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)) (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))))
10.0ms	(/.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)) (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))

series71.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
11.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
30.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)) (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))))
24.0ms	(/.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)) (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))

simplify63.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5415	3204

prune70.0ms

Filtered

103 candidates to 149 candidates (-44.7%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	148	1	149
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	150	9	159

Merged error: 23.5b

Counts

159 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
0.5b	(/.f64 1 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
0.9b	(/.f64 1 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
25.7b	(/.f64 (/.f64 1 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (/.f64 1 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

531×	`times-frac_binary64`
244×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
69×	`associate-/r/_binary64`
52×	`add-exp-log_binary64`
36×	`div-exp_binary64`
35×	`div-inv_binary64`
21×	`associate-/r_binary64` `associate-/l_binary64`
20×	`add-cbrt-cube_binary64`
18×	`flip3--_binary64` `flip--_binary64`
17×	`flip3-+_binary64` `flip-+_binary64`
10×	`1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
2×	`inv-pow_binary64` `pow-flip_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64`

Counts

4 → 364

Calls

4 calls:

4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
6.0ms	(/.f64 1 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
6.0ms	(/.f64 1 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
18.0ms	(/.f64 (/.f64 1 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (/.f64 1 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
6.0ms	(/.f64 1 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
13.0ms	(/.f64 1 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)))
34.0ms	(/.f64 (/.f64 1 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im))) (/.f64 1 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im))))

simplify97.0ms

Algorithm

egg-herbie

Counts

376 → 376

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5040	10845

prune138.0ms

Filtered

191 candidates to 376 candidates (-96.9%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	375	1	376
Fresh	1	4	5
Picked	0	1	1
Done	0	3	3
Total	376	9	385

Merged error: 23.5b

Counts

385 → 9

regimes323.0ms

Accuracy

24.5% (2.2b remaining)

Error of 24.8b against oracle of 22.6b and baseline of 25.5b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	54	54
1	54	54

end0.0ms

sample595.0ms

Algorithm

intervals

Results

364.0ms	8000×	body	80	valid
20.0ms	468×	body	80	invalid

Details

analyze526.0ms

sample22.0ms

simplify191.0ms

prune3.0ms

localize9.0ms

rewrite22.0ms

series48.0ms

simplify50.0ms

prune65.0ms

localize12.0ms

rewrite25.0ms

series65.0ms

simplify49.0ms

prune64.0ms

localize11.0ms

rewrite35.0ms

series71.0ms

simplify63.0ms

prune70.0ms

localize12.0ms

rewrite57.0ms

series64.0ms

simplify97.0ms

prune138.0ms

regimes323.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample595.0ms

Profiling