Details

analyze514.0ms (10.2%)

Algorithm

1×

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

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify160.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	18	30
1	18	30

prune2.0ms (0%)

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: 25.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize13.0ms (0.2%)

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.re y.re) (.f64 x.im y.im))
25.0b	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
9×	`times-frac_binary64_1805`
7×	`add-log-exp_binary64_1838`
5×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
4×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`pow1_binary64_1860` `associate-/l_binary64_1744` `associate-/r_binary64_1743`
2×	`sum-log_binary64_1890` `+-commutative_binary64_1729` `associate-/r/_binary64_1745` `associate-/l/_binary64_1746`
1×	`clear-num_binary64_1798` `div-exp_binary64_1850` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796`

Counts

3 → 53

Calls

3 calls:

10.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
5.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series290.0ms (5.7%)

Counts

3 → 9

Calls

3 calls:

177.0ms	(/.f64 (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
70.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
42.0ms	(+.f64 (.f64 y.re y.re) (.f64 y.im y.im))

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5573	1768

prune336.0ms (6.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	8	63

Merged error: 24.8b

Counts

63 → 8

Compiler

Compiled 6996 to 4198 computations (40% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.9b	(/.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))))
28.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.5b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_1799`
28×	`sqrt-prod_binary64_1815`
25×	`add-sqr-sqrt_binary64_1821`
24×	`times-frac_binary64_1805`
23×	`add-cube-cbrt_binary64_1834`
10×	`unpow-prod-down_binary64_1878` `distribute-lft-out_binary64_1750`
8×	`associate-/r*_binary64_1743`
6×	`pow1_binary64_1860` `sqrt-div_binary64_1816` `add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
5×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`associate-/l*_binary64_1744`
2×	`pow1/2_binary64_1879` `associate-/r/_binary64_1745` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `div-exp_binary64_1850` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796`

Counts

4 → 94

Calls

4 calls:

16.0ms	(/.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))))
9.0ms	(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)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series422.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(/.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))))
75.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
52.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
44.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4963	3187
1	4963	3187

prune239.0ms (4.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	103	11	114

Merged error: 22.5b

Counts

114 → 11

Compiler

Compiled 5432 to 2774 computations (48.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
15.9b	(/.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))))
28.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
28.5b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite51.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_1799`
30×	`sqrt-prod_binary64_1815`
25×	`add-sqr-sqrt_binary64_1821`
24×	`times-frac_binary64_1805`
23×	`add-cube-cbrt_binary64_1834`
12×	`unpow-prod-down_binary64_1878` `distribute-lft-out_binary64_1750`
8×	`associate-/r*_binary64_1743`
6×	`pow1_binary64_1860` `sqrt-div_binary64_1816` `add-log-exp_binary64_1838` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
5×	`flip3-+_binary64_1802` `flip-+_binary64_1773`
3×	`associate-/l*_binary64_1744`
2×	`pow1/2_binary64_1879` `associate-/r/_binary64_1745` `associate-/l/_binary64_1746` `sqrt-pow1_binary64_1817` `rem-sqrt-square_binary64_1812`
1×	`sum-log_binary64_1890` `clear-num_binary64_1798` `div-exp_binary64_1850` `+-commutative_binary64_1729` `frac-2neg_binary64_1810` `cbrt-undiv_binary64_1833` `div-inv_binary64_1796`

Counts

4 → 96

Calls

4 calls:

16.0ms	(/.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))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series401.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

246.0ms	(/.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))))
68.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
45.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5305	3217

prune202.0ms (4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	107	12	119

Merged error: 22.5b

Counts

119 → 12

Compiler

Compiled 4233 to 2545 computations (39.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
0.5b	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
0.8b	(/.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))))
24.6b	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))

rewrite71.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`*-un-lft-identity_binary64_1799`
138×	`times-frac_binary64_1805`
72×	`add-sqr-sqrt_binary64_1821` `add-cube-cbrt_binary64_1834`
34×	`unpow-prod-down_binary64_1878` `distribute-lft-out_binary64_1750`
24×	`associate-/r*_binary64_1743`
17×	`add-exp-log_binary64_1837`
11×	`add-cbrt-cube_binary64_1835` `associate-/r/_binary64_1745`
8×	`div-exp_binary64_1850` `associate-/l*_binary64_1744` `add-log-exp_binary64_1838` `flip3-+_binary64_1802` `flip-+_binary64_1773`
6×	`div-inv_binary64_1796`
5×	`pow1_binary64_1860`
4×	`cbrt-undiv_binary64_1833`
2×	`sum-log_binary64_1890` `clear-num_binary64_1798` `+-commutative_binary64_1729` `rec-exp_binary64_1849` `frac-2neg_binary64_1810` `1-exp_binary64_1843` `associate-/l/_binary64_1746`
1×	`pow-flip_binary64_1873` `inv-pow_binary64_1884`

Counts

4 → 171

Calls

4 calls:

18.0ms	(/.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))))
15.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
9.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))
4.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))

series660.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

439.0ms	(/.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))))
109.0ms	(/.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)) (+.f64 (.f64 x.re y.re) (.f64 x.im y.im)))
74.0ms	(+.f64 (.f64 x.re y.re) (.f64 x.im y.im))
37.0ms	(+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))

simplify128.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5153	7314

prune235.0ms (4.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	183	12	195

Merged error: 22.5b

Counts

195 → 12

Compiler

Compiled 5387 to 2602 computations (51.7% saved)

regimes108.0ms (2.1%)

Compiler: Compiled 1068 to 808 computations (24.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	48
1	26	48

end0.0ms (0%)

sample852.0ms (16.9%)

Algorithm

1×

intervals

Results

336.0ms	8000×	body	128	valid
22.0ms	465×	body	128	invalid

Compiler

Compiled 306 to 229 computations (25.2% saved)

Details

analyze514.0ms (10.2%)

sample22.0ms (0.4%)

simplify160.0ms (3.2%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite24.0ms (0.5%)

series290.0ms (5.7%)

simplify74.0ms (1.5%)

prune336.0ms (6.7%)

localize17.0ms (0.3%)

rewrite45.0ms (0.9%)

series422.0ms (8.4%)

simplify67.0ms (1.3%)

prune239.0ms (4.7%)

localize15.0ms (0.3%)

rewrite51.0ms (1%)

series401.0ms (7.9%)

simplify82.0ms (1.6%)

prune202.0ms (4%)

localize12.0ms (0.2%)

rewrite71.0ms (1.4%)

series660.0ms (13.1%)

simplify128.0ms (2.5%)

prune235.0ms (4.7%)

regimes108.0ms (2.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample852.0ms (16.9%)

Profiling