Details

analyze538.0ms

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

sample20.0ms

Algorithm

intervals

Results

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

simplify317.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	5128	30

prune2.0ms

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: 28.8b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
0.3b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
28.3b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite18.0ms

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

series164.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
39.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
98.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify95.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5717	1814

prune286.0ms

Filtered

51 candidates to 63 candidates (-23.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Merged error: 28.0b

Counts

64 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
16.8b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite34.0ms

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`
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 → 95

Calls

4 calls:

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

series227.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
133.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
25.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
26.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

simplify77.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5186	3239

prune117.0ms

Filtered

78 candidates to 107 candidates (-37.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	103	4	107
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	105	9	114

Merged error: 24.5b

Counts

114 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
16.8b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite40.0ms

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`
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 → 97

Calls

4 calls:

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

series217.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
129.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
23.0ms	(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)))

simplify101.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4917	3269
1	4917	3269

prune136.0ms

Filtered

77 candidates to 109 candidates (-41.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	109	9	118

Merged error: 24.5b

Counts

118 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

16.8b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
30.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
30.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
34.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) 3))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
72×	`times-frac_binary64`
66×	`cbrt-prod_binary64`
58×	`sqrt-prod_binary64`
56×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
52×	`unpow-prod-down_binary64`
30×	`cube-prod_binary64`
22×	`distribute-lft-out_binary64`
10×	`sqrt-div_binary64`
8×	`associate-/r*_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l*_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`cbrt-div_binary64` `rem-cbrt-cube_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `sqr-pow_binary64` `cube-div_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 160

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (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)))
19.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) 3))

series255.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
25.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
22.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
104.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))) 3))

simplify101.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5083	6525

prune136.0ms

Filtered

89 candidates to 172 candidates (-93.3%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	171	10	181

Merged error: 24.5b

Counts

181 → 10

regimes127.0ms

Accuracy

17.1% (2.5b remaining)

Error of 25.3b against oracle of 22.8b and baseline of 25.8b

bsearch1.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	70	105
1	70	105

end0.0ms

sample590.0ms

Algorithm

intervals

Results

358.0ms	8000×	body	80	valid
20.0ms	479×	body	80	invalid

Details

analyze538.0ms

sample20.0ms

simplify317.0ms

prune2.0ms

localize14.0ms

rewrite18.0ms

series164.0ms

simplify95.0ms

prune286.0ms

localize21.0ms

rewrite34.0ms

series227.0ms

simplify77.0ms

prune117.0ms

localize15.0ms

rewrite40.0ms

series217.0ms

simplify101.0ms

prune136.0ms

localize24.0ms

rewrite54.0ms

series255.0ms

simplify101.0ms

prune136.0ms

regimes127.0ms

bsearch1.0ms

simplify4.0ms

end0.0ms

sample590.0ms

Profiling